A **scientific number** comprises two parts:

The exponent of 10 is the number of places the *decimal point must be shifted* to give the number in scientific notation:

Take care when rounding and note that decimal places and significant figures may need trailing zeroes to indicate their accuracy specification e.g. 2.10 is not the same as 2.1 in terms of accuracy being claimed.

Note also that 2.10 has 3 significant figures, but only 2 decimal places.

";
SHOW = ""
for (var i=9; i

"}
else
{if (document.forms[0].elements[item-1].value==COR1 || document.forms[0].elements[item].value==COR2 )
{document.forms[0].elements[item+3].value =
"You got one value right. "+COR2+" x 10 ^{"+COR1+"} was required.

"+ANS+"

"+SHOW+"

" + Feedback%QUESTION.NUMBER% + "

" }
else
{if (document.forms[0].elements[item-1].value!=COR1 && document.forms[0].elements[item].value!=COR2 )
{document.forms[0].elements[item+3].value =
"Your answers were wrong. "+COR2+" x 10 ^{"+COR1+"} was required.

"+ANS+"

"+SHOW+"

" + Feedback%QUESTION.NUMBER% + "

" }
}
}
document.forms[0].elements[item+3].value = QT1 + ET + document.forms[0].elements[item+3].value
}
function question%QUESTION.NUMBER%()
{
A = (1+9*Math.random()).toFixed(2);
B = Math.ceil(2+5*Math.random());
num = Math.round(A*Math.pow(10,B));
QuestionText1%QUESTION.NUMBER% = "Express "+num+" in scientific notation.

"; QuestionText2%QUESTION.NUMBER% = "

*The first input should be correct to two decimal places. Include a minus sign if need be.*";
Correct2%QUESTION.NUMBER% = A;
Correct1%QUESTION.NUMBER% = B;
EquationText%QUESTION.NUMBER%="

"
Feedback%QUESTION.NUMBER% = "The way to do this is to move the decimal point to the left until the resulting number is greater than or equal to 1 and less than 10. In this case we get:

"
for(iB = 1; iB <= B; iB++){
num2 = custRound(num/10,2);
if(iB == 1){Feedback%QUESTION.NUMBER% += num+" = "+num2+" × 10 ^{"+iB+"}

";}else{Feedback%QUESTION.NUMBER% += num+"× 10 ^{"+(iB-1)+"} = "+num2+" × 10 ^{"+iB+"}

";}
num = num2;
}
Feedback%QUESTION.NUMBER% += "

Of course you do not need to write all this out if you don't want to: you can simply move the decimal point "+B+" places to the left counting them carefully.

Finally, check the format of the numbers required, including trailing zeros if needed.

" document.write(QuestionText1%QUESTION.NUMBER%+EquationText%QUESTION.NUMBER%); td = "" document.write(""+td+""+td+""+td+"x 10"+td+"

"+""+"

") } // Template updated and developed by Daniel Nichols & Martin Greenhow, Brunel University, July 2002, working // on original templates authored by Dominic Smith of Brunel University, July 2001, with // valuable contributions from Professor David Hewitt of Monash University, Australia. ]]>

A **scientific number** comprises two parts:

The exponent of 10 is the number of places the *decimal point must be shifted* to give the number in scientific notation:

Take care when rounding and note that decimal places and significant figures may need trailing zeroes to indicate their accuracy specification e.g. 2.10 is not the same as 2.1 in terms of accuracy being claimed.

Note also that 2.10 has 3 significant figures, but only 2 decimal places.

";
SHOW = ""
for (var i=9; i

"}
else
{if (document.forms[0].elements[item-1].value==COR1 || document.forms[0].elements[item].value==COR2 )
{document.forms[0].elements[item+3].value =
"You got one value right. "+COR2+" x 10 ^{"+COR1+"} was required.

"+ANS+"

"+SHOW+"

" + Feedback%QUESTION.NUMBER% + "

" }
else
{if (document.forms[0].elements[item-1].value!=COR1 && document.forms[0].elements[item].value!=COR2 )
{document.forms[0].elements[item+3].value =
"Your answers were wrong. "+COR2+" x 10 ^{"+COR1+"} was required.

"+ANS+"

"+SHOW+"

" + Feedback%QUESTION.NUMBER% + "

" }
}
}
document.forms[0].elements[item+3].value = QT1 + ET + document.forms[0].elements[item+3].value
}
function question%QUESTION.NUMBER%()
{
A = (1+9*Math.random()).toFixed(2);
B = -Math.ceil(2+5*Math.random());
num = (A*Math.pow(10,B)).toFixed(-(B-2));
QuestionText1%QUESTION.NUMBER% = "Express "+num+" in scientific notation.

"; QuestionText2%QUESTION.NUMBER% = "

*The first input should be correct to two decimal places. Include a minus sign if need be.*";
Correct2%QUESTION.NUMBER% = A;
Correct1%QUESTION.NUMBER% = B;
EquationText%QUESTION.NUMBER%="

"
Feedback%QUESTION.NUMBER% = "The way to do this is to move the decimal point to the right until the resulting number is greater than or equal to 1 and less than 10. In this case we get:

"
for(iB = -1; iB >= B; iB--){
num2 = (num*10).toFixed(-B+iB+2);
if(iB == -1){Feedback%QUESTION.NUMBER% += num+" = "+num2+" × 10 ^{"+iB+"}

";}else{Feedback%QUESTION.NUMBER% += num+" × 10 ^{"+(iB+1)+"} = "+num2+" × 10 ^{"+iB+"}

";}
num = num2;
}
move=Math.abs(B);
Feedback%QUESTION.NUMBER% += "

Of course you do not need to write all this out if you don't want to: you can simply move the decimal point "+move+" places to the right counting them carefully.

Finally, check the format of the numbers required, including trailing zeros if needed.

" document.write(QuestionText1%QUESTION.NUMBER%+EquationText%QUESTION.NUMBER%); td = "" document.write(""+td+""+td+""+td+"x 10"+td+"

"+""+"

") } // Template updated and developed by Daniel Nichols & Martin Greenhow, Brunel University, July 2002, working // on original templates authored by Dominic Smith of Brunel University, July 2001, with // valuable contributions from Professor David Hewitt of Monash University, Australia. ]]>

A **scientific number** comprises two parts:

The exponent of 10 is the number of places the *decimal point must be shifted* to give the number in scientific notation:

Take care when rounding and note that decimal places and significant figures may need trailing zeroes to indicate their accuracy specification e.g. 2.10 is not the same as 2.1 in terms of accuracy being claimed.

Note also that 2.10 has 3 significant figures, but only 2 decimal places.

"+Table%QUESTION.NUMBER%+"";
SHOW = ""
for (var i=9; i

"}
else
{if (document.forms[0].elements[item-1].value==COR1 || document.forms[0].elements[item].value==COR2 )
{document.forms[0].elements[item+3].value =
"You got one value right. "+COR2+" x 10 ^{"+COR1+"} was required.

"+ANS+"

"+SHOW+"

" + Feedback%QUESTION.NUMBER% + "

" }
else
{if (document.forms[0].elements[item-1].value!=COR1 && document.forms[0].elements[item].value!=COR2 )
{document.forms[0].elements[item+3].value =
"Your answers were wrong. "+COR2+" x 10 ^{"+COR1+"} was required.

"+ANS+"

"+SHOW+"

" + Feedback%QUESTION.NUMBER% + "

" }
}
}
document.forms[0].elements[item+3].value = QT1 + ET + document.forms[0].elements[item+3].value
}
function question%QUESTION.NUMBER%()
{
myNumArray = displayarray( 2, -6, 6, 0);
B = myNumArray[0];
E = myNumArray[1];
n = Math.ceil(4*Math.random());
m1 = Math.ceil(n+4*Math.random());
m2= Math.ceil(n+4*Math.random());
A = (1+9*Math.random()).toFixed(m1);
D = (1+9*Math.random()).toFixed(m2);
signA = Math.ceil(2*Math.random());
signD = Math.ceil(2*Math.random());
if(signA == 1){A = -A};
if(signD == 1){D = -D};
decsigfigchoice = Math.ceil(2*Math.random());
if(n == 1){decimal_places = "decimal place"; significant_figures ="significant figure"}else{decimal_places = "decimal places"; significant_figures ="significant figures"}
if(decsigfigchoice == 1){decsigfig = "decimal";decsigfigword = decimal_places;}else{decsigfig = "sigfig";decsigfigword = significant_figures};
QuestionText1%QUESTION.NUMBER% = "Evaluate "+A+" x 10^{"+B+"} divided by "+D+" x 10^{"+E+"}

*Input your answer in scientific notation, with minus signs where necessary. The first input should be correct to "+n+" "+decsigfigword+".*

";
QuestionText2%QUESTION.NUMBER% = "";
num=A*Math.pow(10,B)/(D*Math.pow(10,E));
Correct2%QUESTION.NUMBER% = scientific_number(num,0,n,decsigfig);
Correct1%QUESTION.NUMBER% = scientific_number(num,1);
digitsdivision=A/D;
shortdivision=digitsdivision.toFixed(2+4);
tensdivision=scientific_number(Math.pow(10,B)/Math.pow(10,E),1);
power=scientific_number(digitsdivision,1);
td = ""
th = ""
Table%QUESTION.NUMBER%="";
Table%QUESTION.NUMBER% += ""+th+"Result"+th+"Explanation"+td+"("+A+" × 10^{"+B+"}) ÷ ("+D+" × 10^{"+E+"})"+""+td+"*original expression*"+""+td+"= ("+A+"÷"+D+")× (10^{"+B+"}÷10^{"+E+"})"+""+td+" *the terms are grouped so digit terms are next to each other followed by the power of 10 index*"+""+td+"= "+shortdivision+"× 10^{"+tensdivision+"}"+""+td+"*the digit terms are divided in the normal way and the exponents (powers of 10) are subrtacted*"+"";
if(power==0){Table%QUESTION.NUMBER%+=""+td+" = **"+Correct2%QUESTION.NUMBER%+"× 10 ^{"+Correct1%QUESTION.NUMBER%+"}"+""+td+"number "+shortdivision+" is converted to scientific notation according to the accuracy specification, i.e. "+n+" "+decsigfigword+", giving the correct scientific notation "+"**

" Feedback%QUESTION.NUMBER% = "" document.write(QuestionText1%QUESTION.NUMBER%+EquationText%QUESTION.NUMBER%); document.write(QuestionText2%QUESTION.NUMBER%); document.write(""+td+""+td+""+td+"x 10"+td+"

") } // Template updated and developed by Daniel Nichols & Martin Greenhow, Brunel University, July 2002, working // on original templates authored by Dominic Smith of Brunel University, July 2001, with // valuable contributions from Professor David Hewitt of Monash University, Australia. ]]>

A **scientific number** comprises two parts:

*decimal point must be shifted* to give the number in scientific notation:

Take care when rounding and note that decimal places and significant figures may need trailing zeroes to indicate their accuracy specification e.g. 2.10 is not the same as 2.1 in terms of accuracy being claimed.

Note also that 2.10 has 3 significant figures, but only 2 decimal places.

"+Table%QUESTION.NUMBER%+"";
SHOW = ""
for (var i=9; i

"}
else
{if (document.forms[0].elements[item-1].value==COR1 || document.forms[0].elements[item].value==COR2 )
{document.forms[0].elements[item+3].value =
"You got one value right. "+COR2+" x 10 ^{"+COR1+"} was required.

"+ANS+"

"+SHOW+"

" + Feedback%QUESTION.NUMBER% + "

" }
else
{if (document.forms[0].elements[item-1].value!=COR1 && document.forms[0].elements[item].value!=COR2 )
{document.forms[0].elements[item+3].value =
"Your answers were wrong. "+COR2+" x 10 ^{"+COR1+"} was required.

"+ANS+"

"+SHOW+"

" + Feedback%QUESTION.NUMBER% + "

" }
}
}
document.forms[0].elements[item+3].value = QT1 + ET + document.forms[0].elements[item+3].value
}
function question%QUESTION.NUMBER%()
{
myNumArray = displayarray( 2, -6, 6, 0);
B = myNumArray[0];
E = myNumArray[1];
n = Math.ceil(4*Math.random());
m1 = Math.ceil(n+4*Math.random());
m2= Math.ceil(n+4*Math.random());
A = (1+9*Math.random()).toFixed(m1);
D = (1+9*Math.random()).toFixed(m2);
signA = Math.ceil(2*Math.random());
signD = Math.ceil(2*Math.random());
if(signA == 1){A = -A};
if(signD == 1){D = -D};
decsigfigchoice = Math.ceil(2*Math.random());
if(n == 1){decimal_places = "decimal place"; significant_figures ="significant figure"}else{decimal_places = "decimal places"; significant_figures ="significant figures"}
if(decsigfigchoice == 1){decsigfig = "decimal";decsigfigword = decimal_places;}else{decsigfig = "sigfig";decsigfigword = significant_figures};
QuestionText1%QUESTION.NUMBER% = "Evaluate the product of "+A+" x 10^{"+B+"} and "+D+" x 10^{"+E+"}

*Input your answer in scientific notation, with minus signs where necessary. The first input should be correct to "+n+" "+decsigfigword+".*

";
QuestionText2%QUESTION.NUMBER% = "";
num=A*Math.pow(10,B)*D*Math.pow(10,E);
Correct2%QUESTION.NUMBER% = scientific_number(num,0,n,decsigfig);
Correct1%QUESTION.NUMBER% = scientific_number(num,1);
digitsproduct=A*D;
shortproduct=digitsproduct.toFixed(2+4);
tensproduct=scientific_number(Math.pow(10,B)*Math.pow(10,E),1);
power=scientific_number(digitsproduct,1);
td = ""
th = ""
Table%QUESTION.NUMBER%="";
Table%QUESTION.NUMBER% = ""+th+"Result"+th+"Explanation"+td+"("+A+" × 10^{"+B+"})("+D+" × 10^{"+E+"})"+""+td+"*original expression*"+""+td+"= ("+A+"×"+D+")(10^{"+B+"}×10^{"+E+"})"+""+td+" *the terms are grouped so digit terms are next to each other followed by the power of 10 index*"+""+td+"= "+shortproduct+"×10^{"+tensproduct+"}"+""+td+"*the digit terms are multiplied in the normal way and the exponents (powers of 10) are added*"+"";
if(power==0){Table%QUESTION.NUMBER%+=""+td+" = **"+Correct2%QUESTION.NUMBER%+"×10 ^{"+Correct1%QUESTION.NUMBER%+"}"+""+td+"number "+shortproduct+" is converted to scientific notation according to the accuracy specification, i.e. "+n+" "+decsigfigword+", giving the correct scientific notation "+"**

" Feedback%QUESTION.NUMBER% = "" document.write(QuestionText1%QUESTION.NUMBER%+EquationText%QUESTION.NUMBER%); document.write(QuestionText2%QUESTION.NUMBER%); document.write(""+td+""+td+""+td+"x 10"+td+"

") } // Template updated and developed by Daniel Nichols & Martin Greenhow, Brunel University, July 2002, working // on original templates authored by Dominic Smith of Brunel University, July 2001, with // valuable contributions from Professor David Hewitt of Monash University, Australia. ]]>

A **scientific number** comprises two parts:

*decimal point must be shifted* to give the number in scientific notation:

Take care when rounding and note that decimal places and significant figures may need trailing zeroes to indicate their accuracy specification e.g. 2.10 is not the same as 2.1 in terms of accuracy being claimed.

Note also that 2.10 has 3 significant figures, but only 2 decimal places.

";
SHOW = Feedback%QUESTION.NUMBER%;
for (var i=5; i**Solution:** "+SHOW+"

"}
else
/////////////////////// Dis1//////////////////////////
{if (document.forms[0].elements[item].value==DISA )
{document.forms[0].elements[item+3].value =
"D1) Your answer "+document.forms[0].elements[item].value+", should have been "+COR+"

"+ANS+"

"+SHOW+"

" }
else
/////////////////////// Dis2//////////////////////////
{if (document.forms[0].elements[item].value==DISB )
{document.forms[0].elements[item+3].value =
"D2) Your answer "+document.forms[0].elements[item].value+", should have been "+COR+"

"+ANS+"

"+SHOW+"

" }
else
/////////////////////// Dis3//////////////////////////
{if (document.forms[0].elements[item].value==DISC )
{document.forms[0].elements[item+3].value =
"D3) Your answer "+document.forms[0].elements[item].value+", should have been "+COR+"

"+ANS+"

"+SHOW+"

" }
else
/////////////////////// Dis4//////////////////////////
{if (document.forms[0].elements[item].value==DISD )
{document.forms[0].elements[item+3].value =
"D4) Your answer "+document.forms[0].elements[item].value+", should have been "+COR+"

"+ANS+"

"+SHOW+"

" }
else
/////////////////////// Dis5//////////////////////////
{if (document.forms[0].elements[item].value==DISE )
{document.forms[0].elements[item+3].value =
"D5) Your answer "+document.forms[0].elements[item].value+", should have been "+COR+"

"+ANS+"

"+SHOW+"

" }
else
/////////////////////// Dis6//////////////////////////
{if (document.forms[0].elements[item].value==DISF )
{document.forms[0].elements[item+3].value =
"D6) Your answer "+document.forms[0].elements[item].value+", should have been "+COR+"

"+ANS+"

"+SHOW+"

" }
else
{document.forms[0].elements[item+3].value =
"Your answer "+document.forms[0].elements[item].value+", should have been "+COR+"

"+ANS+"

"+SHOW+" "}
document.forms[0].elements[item+3].value = QT+ document.forms[0].elements[item+3].value
}}}}}}}
function question%QUESTION.NUMBER%()
{
A = (1+9*Math.random()).toFixed(2);
B = Math.ceil(2+5*Math.random());
num = Math.round(A*Math.pow(10,B));
num1 = Math.round(A*Math.pow(10,B-1));
QuestionText%QUESTION.NUMBER% = "Express "+A+" × 10 ^{"+B+"} as a decimal (i.e. ordinary) number.

"; QuestionText2%QUESTION.NUMBER% = "

*Give your answer exactly.*";
EquationText%QUESTION.NUMBER%="

";
Correct%QUESTION.NUMBER% = num;
Distractor1%QUESTION.NUMBER% = num1;
Distractor2%QUESTION.NUMBER% = "";
Distractor3%QUESTION.NUMBER% = "";
Distractor4%QUESTION.NUMBER% = "";
Distractor5%QUESTION.NUMBER% = "";
Distractor6%QUESTION.NUMBER% = "";
Feedback%QUESTION.NUMBER% = "The way to do this is to successively multiply by 10, as follows:

"
for(iB = B; iB >= 1; iB--){
A1 = custRound(A*10,2);
if(iB != 1){Feedback%QUESTION.NUMBER% += A+" × 10 ^{"+iB+"} = "+A1+" × 10 ^{"+(iB-1)+"}

";}else{Feedback%QUESTION.NUMBER% += A+" × 10 ^{"+iB+"} = "+A1+"

";}
A = A1;
}
Feedback%QUESTION.NUMBER% += "

Of course you do not need to write all this out if you don't want to: you can simply move the decimal point "+B+" places to the right, adding zeroes as required, and counting carefully.

"
document.write(QuestionText%QUESTION.NUMBER%);
document.write("")
document.write(QuestionText2%QUESTION.NUMBER%);
document.write("")
}
if (document.forms[0].name=="FEEDBACK")
{}
else
{question%QUESTION.NUMBER%()}
]]>

"+""+"

") } // Template updated and developed by Daniel Nichols & Martin Greenhow, Brunel University, July 2004, working // on original templates authored by Dominic Smith of Brunel University, July 2001, with // valuable contributions from Professor David Hewitt of Monash University, Australia. ]]>

A **scientific number** comprises two parts:

*decimal point must be shifted* to give the number in scientific notation:

Take care when rounding and note that decimal places and significant figures may need trailing zeroes to indicate their accuracy specification e.g. 2.10 is not the same as 2.1 in terms of accuracy being claimed.

Note also that 2.10 has 3 significant figures, but only 2 decimal places.

";
SHOW = Feedback%QUESTION.NUMBER%;
for (var i=5; i**Solution:** "+SHOW+"

"}
else
/////////////////////// Dis1//////////////////////////
{if (document.forms[0].elements[item].value==DISA )
{document.forms[0].elements[item+3].value =
"D1) Your answer "+document.forms[0].elements[item].value+", should have been "+COR+"

"+ANS+"

"+SHOW+"

" }
else
/////////////////////// Dis2//////////////////////////
{if (document.forms[0].elements[item].value==DISB )
{document.forms[0].elements[item+3].value =
"D2) Your answer "+document.forms[0].elements[item].value+", should have been "+COR+"

"+ANS+"

"+SHOW+"

" }
else
/////////////////////// Dis3//////////////////////////
{if (document.forms[0].elements[item].value==DISC )
{document.forms[0].elements[item+3].value =
"D3) Your answer "+document.forms[0].elements[item].value+", should have been "+COR+"

"+ANS+"

"+SHOW+"

" }
else
/////////////////////// Dis4//////////////////////////
{if (document.forms[0].elements[item].value==DISD )
{document.forms[0].elements[item+3].value =
"D4) Your answer "+document.forms[0].elements[item].value+", should have been "+COR+"

"+ANS+"

"+SHOW+"

" }
else
/////////////////////// Dis5//////////////////////////
{if (document.forms[0].elements[item].value==DISE )
{document.forms[0].elements[item+3].value =
"D5) Your answer "+document.forms[0].elements[item].value+", should have been "+COR+"

"+ANS+"

"+SHOW+"

" }
else
/////////////////////// Dis6//////////////////////////
{if (document.forms[0].elements[item].value==DISF )
{document.forms[0].elements[item+3].value =
"D6) Your answer "+document.forms[0].elements[item].value+", should have been "+COR+"

"+ANS+"

"+SHOW+"

" }
else
{document.forms[0].elements[item+3].value =
"Your answer "+document.forms[0].elements[item].value+", should have been "+COR+"

"+ANS+"

"+SHOW+" "}
document.forms[0].elements[item+3].value = QT+ document.forms[0].elements[item+3].value
}}}}}}}
function question%QUESTION.NUMBER%()
{
A = (1+9*Math.random()).toFixed(2);
B = -Math.ceil(2+5*Math.random());
num = (A*Math.pow(10,B)).toFixed(2-B);
QuestionText%QUESTION.NUMBER% = "Express "+A+" × 10 ^{"+B+"} as a decimal (i.e. ordinary) number.

"; QuestionText2%QUESTION.NUMBER% = "

*Give your answer exactly.*";
EquationText%QUESTION.NUMBER%="

";
Correct%QUESTION.NUMBER% = num;
Distractor1%QUESTION.NUMBER% = "";
Distractor2%QUESTION.NUMBER% = "";
Distractor3%QUESTION.NUMBER% = "";
Distractor4%QUESTION.NUMBER% = "";
Distractor5%QUESTION.NUMBER% = "";
Distractor6%QUESTION.NUMBER% = "";
Feedback%QUESTION.NUMBER% = "The way to do this is to successively divide by 10, as follows:

"
count_places = 1;
for(iB = B; iB <= -1; iB++){
count_places+=1;
A1 = (A/10).toFixed(1+count_places);
if(iB != -1){Feedback%QUESTION.NUMBER% += A+" × 10 ^{"+iB+"} = "+A1+" × 10 ^{"+(iB+1)+"}

";}else{Feedback%QUESTION.NUMBER% += A+" × 10 ^{"+iB+"} = "+A1+"

";}
A = A1;
}
move=Math.abs(B);
Feedback%QUESTION.NUMBER% += "

Of course you do not need to write all this out if you don't want to: you can simply move the decimal point "+move+" places to the left, adding zeroes as required, and counting carefully.

"
document.write(QuestionText%QUESTION.NUMBER%);
document.write("")
document.write(QuestionText2%QUESTION.NUMBER%);
document.write("")
}
if (document.forms[0].name=="FEEDBACK")
{}
else
{question%QUESTION.NUMBER%()}
]]>

"+""+"

") } // Template updated and developed by Daniel Nichols & Martin Greenhow, Brunel University, July 2004, working // on original templates authored by Dominic Smith of Brunel University, July 2001, with // valuable contributions from Professor David Hewitt of Monash University, Australia. ]]>

A **scientific number** comprises two parts:

*decimal point must be shifted* to give the number in scientific notation:

Take care when rounding and note that decimal places and significant figures may need trailing zeroes to indicate their accuracy specification e.g. 2.10 is not the same as 2.1 in terms of accuracy being claimed.

Note also that 2.10 has 3 significant figures, but only 2 decimal places.

";
SHOW = ""
for (var i=9; i

"}
else
{if (document.forms[0].elements[item-1].value==COR1 || document.forms[0].elements[item].value==COR2 )
{document.forms[0].elements[item+3].value =
"You got one value right. "+COR2+" x 10 ^{"+COR1+"} was required.

"+ANS+"

"+SHOW+"

" + Feedback%QUESTION.NUMBER% + "

" }
else
{if (document.forms[0].elements[item-1].value!=COR1 && document.forms[0].elements[item].value!=COR2 )
{document.forms[0].elements[item+3].value =
"Your answers were wrong. "+COR2+" x 10 ^{"+COR1+"} was required.

"+ANS+"

"+SHOW+"

" + Feedback%QUESTION.NUMBER% + "

" }
}
}
document.forms[0].elements[item+3].value = QT1 + ET + document.forms[0].elements[item+3].value
}
function question%QUESTION.NUMBER%()
{
myNumArray = displayarray( 2, -6, 6, 0);
indexArray = displayarray( 2, -6, 6, 0);
B = myNumArray[0];
if(B == 1){B=7};
E = myNumArray[1];
n = Math.ceil(4*Math.random());
// index = Math.ceil(4*Math.random())+1;
nwidth=getFontSize()/16*80
nheight=getFontSize()/16*100
m1=""
xindex = m1 + m2 + m3 + m4;
//sign = displayarray( 1, -1, 1, 0);
m1 = Math.ceil(n+4*Math.random());
m2= Math.ceil(n+4*Math.random());
A = (1+9*Math.random()).toFixed(m1);
D = (1+9*Math.random()).toFixed(m2);
signA = Math.ceil(2*Math.random());
signD = Math.ceil(2*Math.random());
//if(signA == 1){A = -A};
if(signD == 1){D = -D};
decsigfigchoice = Math.ceil(2*Math.random());
if(n == 1){decimal_places = "decimal place"; significant_figures ="significant figure"}else{decimal_places = "decimal places"; significant_figures ="significant figures"}
if(decsigfigchoice == 1){decsigfig = "decimal";decsigfigword = decimal_places;}else{decsigfig = "sigfig";decsigfigword = significant_figures};
// QuestionText1%QUESTION.NUMBER% = "If *x* = "+A+" x 10^{"+B+"} evaluate

" + xindex + "

*Input your answer in scientific notation correct to "+n+" "+decsigfigword+", with minus signs where necessary.*

";
QuestionText1%QUESTION.NUMBER% = "If *x* = "+A+" x 10^{"+B+"} evaluate

"; QuestionText2%QUESTION.NUMBER% = "

*Input your answer in scientific notation, with minus signs where necessary. The first input should be correct to "+n+" "+decsigfigword+".*

";
num=Math.pow(A*Math.pow(10,B),(p/q));
Correct2%QUESTION.NUMBER% = scientific_number(num,0,n,decsigfig);
Correct1%QUESTION.NUMBER% = scientific_number(num,1);
EquationText%QUESTION.NUMBER%= xindex+"

"
Feedback%QUESTION.NUMBER% = ""
document.write(QuestionText1%QUESTION.NUMBER%+EquationText%QUESTION.NUMBER%);
td = ""
document.write(""+td+""+td+""+td+"x 10"+td+"

"+""+"

") } // Template updated and developed by Daniel Nichols & Martin Greenhow, Brunel University, July 2002, working // on original templates authored by Dominic Smith of Brunel University, July 2001, with // valuable contributions from Professor David Hewitt of Monash University, Australia. ]]>

A **scientific number** comprises two parts:

*decimal point must be shifted* to give the number in scientific notation:

Note also that 2.10 has 3 significant figures, but only 2 decimal places.

"+Table%QUESTION.NUMBER%+"";
SHOW = ""
for (var i=9; i

"}
else
{if (document.forms[0].elements[item-1].value==COR1 || document.forms[0].elements[item].value==COR2 )
{document.forms[0].elements[item+3].value =
"You got one value right. "+COR2+" x 10 ^{"+COR1+"} was required.

"+ANS+"

"+SHOW+"

" + Feedback%QUESTION.NUMBER% + "

" }
else
{if (document.forms[0].elements[item-1].value!=COR1 && document.forms[0].elements[item].value!=COR2 )
{document.forms[0].elements[item+3].value =
"Your answers were wrong. "+COR2+" x 10 ^{"+COR1+"} was required.

"+ANS+"

"+SHOW+"

" + Feedback%QUESTION.NUMBER% + "

" }
}
}
document.forms[0].elements[item+3].value = QT1 + ET + document.forms[0].elements[item+3].value
}
function question%QUESTION.NUMBER%()
{
myNumArray = displayarray( 2, -6, 6, 0);
B = myNumArray[0];
if(B == 1){B=7};
E = myNumArray[1];
n = Math.ceil(4*Math.random());
index = Math.ceil(4*Math.random())+1;
sign = displayarray( 1, -1, 1, 0);
index = index*sign;
m1 = Math.ceil(n+4*Math.random());
m2= Math.ceil(n+4*Math.random());
A = (1+9*Math.random()).toFixed(m1);
D = (1+9*Math.random()).toFixed(m2);
signA = Math.ceil(2*Math.random());
signD = Math.ceil(2*Math.random());
//if(signA == 1){A = -A};
if(signD == 1){D = -D};
decsigfigchoice = Math.ceil(2*Math.random());
if(n == 1){decimal_places = "decimal place"; significant_figures ="significant figure"}else{decimal_places = "decimal places"; significant_figures ="significant figures"}
if(decsigfigchoice == 1){decsigfig = "decimal";decsigfigword = decimal_places;}
else{decsigfig = "sigfig";decsigfigword = significant_figures};
QuestionText1%QUESTION.NUMBER% = "Evaluate "+A+" x 10^{"+B+"} raised to the power of "+index+" .

";
QuestionText2%QUESTION.NUMBER% = "";
num=Math.pow(A*Math.pow(10,B),index);
Correct2%QUESTION.NUMBER% = scientific_number(num,0,n,decsigfig);
Correct1%QUESTION.NUMBER% = scientific_number(num,1);
digitpower=Math.pow(A,index);
tensdivision=scientific_number(Math.pow(10,B)/Math.pow(10,E),1);
power=scientific_number(digitpower,1);
if(digitpower<1 && Math.abs(power)+n>5){digitlength=Math.abs(power)+n+1}
else{digitlength=6}
shortdigitpower=digitpower.toFixed(digitlength);
powers=B*index;
penultimateline="";
if(power==0){penultimateline=Correct2%QUESTION.NUMBER%+ "×" + 10+"^{"+Correct1%QUESTION.NUMBER%+"}"}
else{penultimateline=Correct2%QUESTION.NUMBER%+ "×" + 10+"^{"+power+"}"+ "×" + 10+"^{"+powers+"}"};
td = ""
th = ""
Table%QUESTION.NUMBER%="";
Table%QUESTION.NUMBER% += ""+th+"..........................Result.........................."+th+"Explanation"+td+"("+A+" x 10^{"+B+"})^{"+index+"}"+""+td+"*original expression*"+""+td+"= ("+A+")^{"+index+"} x (10^{"+B+"})^{"+index+"}"+""+td+" *the product of two numbers raised to the power of "+index+" is broken down into the product of the first term raised to the power of "+index+" and the second term raised to the power of "+index+"*"+""+td+"= "+shortdigitpower+"×10^{"+powers+"}"+""+td+"*the digit term raised to the power of "+index+" is calculated in the normal way and the exponents of 10 are multiplied*"+"";
if(power==0){Table%QUESTION.NUMBER%+=""+td+"= **"+penultimateline+"**"+""+td+"*number "+shortdigitpower+" is converted to scientific notation according to the accuracy specification, i.e. "+n+" "+decsigfigword+", giving the correct scientific notation * "+"";}
else{Table%QUESTION.NUMBER%+=""+td+"= "+penultimateline+""+""+td+"*number "+shortdigitpower+" is converted to scientific notation according to the accuracy specification, i.e. "+n+" "+decsigfigword+"*"+""+td+" = **"+Correct2%QUESTION.NUMBER%+"×10 ^{"+Correct1%QUESTION.NUMBER%+"}"+""+td+"the exponents are added giving the correct scientific notation "+"**

" +Correct1%QUESTION.NUMBER%+"

" +Correct2%QUESTION.NUMBER%; EquationText%QUESTION.NUMBER%="

" Feedback%QUESTION.NUMBER% = "" document.write(QuestionText1%QUESTION.NUMBER%+EquationText%QUESTION.NUMBER%); document.write(QuestionText2%QUESTION.NUMBER%); document.write(""+td+""+td+""+td+"x 10"+td+"

") } // Template updated and developed by Daniel Nichols & Martin Greenhow, Brunel University, July 2002, working // on original templates authored by Dominic Smith of Brunel University, July 2001, with // valuable contributions from Professor David Hewitt of Monash University, Australia. ]]>

A **scientific number** comprises two parts:

*decimal point must be shifted* to give the number in scientific notation:

Note also that 2.10 has 3 significant figures, but only 2 decimal places.

"+table+"";
SHOW = ""
for (var i=9; i

"}
else
{if (document.forms[0].elements[item-1].value==COR1 || document.forms[0].elements[item].value==COR2 )
{document.forms[0].elements[item+3].value =
"You got one value right. "+COR2+" x 10 ^{"+COR1+"} was required.

"+ANS+"

"+SHOW+"

" + Feedback%QUESTION.NUMBER% + "

" }
else
{if (document.forms[0].elements[item-1].value!=COR1 && document.forms[0].elements[item].value!=COR2 )
{document.forms[0].elements[item+3].value =
"Your answers were wrong. "+COR2+" x 10 ^{"+COR1+"} was required.

"+ANS+"

"+SHOW+"

" + Feedback%QUESTION.NUMBER% + "

" }
}
}
document.forms[0].elements[item+3].value = QT1 + ET + document.forms[0].elements[item+3].value
}
function question%QUESTION.NUMBER%()
{
myNumArray = displayarray( 2, -6, 6, 0);
B = myNumArray[0];
E = myNumArray[1];
n = Math.ceil(4*Math.random());
m1 = Math.ceil(n+4*Math.random());
m2= Math.ceil(n+4*Math.random());
n1=m1-1;
A = (1+9*Math.random()).toFixed(m1);
D = (1+9*Math.random()).toFixed(m2);
signA = Math.ceil(2*Math.random());
signD = Math.ceil(2*Math.random());
//if(signA == 1){A = -A};
if(signD == 1){D = -D};
decsigfigchoice = Math.ceil(2*Math.random());
if(n == 1){decimal_places = "decimal place"; significant_figures ="significant figure"}else{decimal_places = "decimal places"; significant_figures ="significant figures"}
if(decsigfigchoice == 1){decsigfig = "decimal";decsigfigword = decimal_places;}else{decsigfig = "sigfig";decsigfigword = significant_figures};
QuestionText1%QUESTION.NUMBER% = "Evaluate the positive square root of "+A+" x 10^{"+B+"}.

";
QuestionText2%QUESTION.NUMBER% = "";
num=Math.sqrt(A*Math.pow(10,B));
Correct2%QUESTION.NUMBER% = scientific_number(num,0,n,decsigfig);
Correct1%QUESTION.NUMBER% = scientific_number(num,1);
nwidth=getFontSize()/16*350
nheight=getFontSize()/16*55
m1=""
e2=""
EquationText1%QUESTION.NUMBER% = m1 + m2 + m3 + e1;
EquationText2%QUESTION.NUMBER% = m1 + m2 + m3 + e2;
sqrteven=Math.sqrt(A);
shortsqrteven=sqrteven.toFixed(2+4);
power1=B/2;
power2=B-1;
power3=power2/2;
digitnumbermultiplied=A*10-0;
digitmultiplied=digitnumbermultiplied.toFixed(n1);
sqrtodd=Math.sqrt(digitnumbermultiplied);
shortsqrtodd=sqrtodd.toFixed(2+4);
td = ""
th = ""
Table%QUESTION.NUMBER% = ""+th+"Result"+th+"Explanation"+td+""+EquationText1%QUESTION.NUMBER%+""+td+"*original expression*"+""+td+EquationText2%QUESTION.NUMBER%+""+td+" *the square root of a product is broken down into the product of two square roots *"+""+td+"= ("+A+")^{1/2}×(10^{"+B+"})^{1/2}"+""+td+" * taking the square root is the same as raising the number to the one-half power*"+""+td+"= "+shortsqrteven+"×10^{"+power1+"}"+""+td+"*the square root of the digit term is taken and the exponents of 10 are multiplied*"+""+td+" = **"+Correct2%QUESTION.NUMBER%+"×10 ^{"+Correct1%QUESTION.NUMBER%+"}"+""+td+"number is converted to scientific notation according to the accuracy specification, i.e. "+n+" "+decsigfigword+", giving the correct scientific notation "+"**

" +Correct1%QUESTION.NUMBER%+"

" +Correct2%QUESTION.NUMBER%; EquationText%QUESTION.NUMBER%="

" Feedback%QUESTION.NUMBER% = "" document.write(QuestionText1%QUESTION.NUMBER%+EquationText%QUESTION.NUMBER%); document.write(QuestionText2%QUESTION.NUMBER%); document.write(""+td+""+td+""+td+"x 10"+td+"

") } // Template updated and developed by Daniel Nichols & Martin Greenhow, Brunel University, July 2002, working // on original templates authored by Dominic Smith of Brunel University, July 2001, with // valuable contributions from Professor David Hewitt of Monash University, Australia. ]]>