var index1=Math.round(Math.random()*(3-1))+1; var question1=new Array(3); var truevalue1=new Array(3); question1[0]='

'; truevalue1[0]='3.94'; question1[1]='

'; truevalue1[1]='273.0'; question1[2]='

'; truevalue1[2]='269'; question1[3]='

'; truevalue1[3]='15,900'; window.document.write('

Significant Figures and Calculations

A. Addition and Subtraction:
When numbers are added and/or subtracted, the answer is rounded off to the decimal place that has the greatest uncertainty.

For example, let´s add the following numbers, and then round off the answer appropriately.

296.65 + 56.8 + 9.5508 = ?

What are the uncertainties of these measurements? The uncertainty is always found in the last significant digit of the measurement. Therefore, the uncertainties are:

296.65 ą 0.01

56.8 ą 0.1

9.5508 ą 0.0001

Thus, the answer must be rounded off to the tenths place. This can also be seen if the numbers are placed in column form.

Let´s try a few more examples. Type in the rounded off answer.

' + question1[index1] +'

'); var index2=Math.round(Math.random()*(3-1))+1; var question2=new Array(3); var truevalue2=new Array(3); question2[0]='

24.76 x 21.0 =

'; truevalue2[0]='520'; question2[1]='

24.76 x 21.0 =

'; truevalue2[1]='520'; question2[2]='

163.00
	=
0.273

'; truevalue2[2]='9,600'; question2[3]='

9.200
	=
1,431.8

'; truevalue2[3]='9,600'; window.document.write('

B. Multiplication and Division:
When numbers are multiplied and/or divided, the number of significant figures in the answer is equal to the smallest number of significant figures in any of the measurements.

Let´s multiply together two numbers and see how to round off the answer that is produced by the calculator.

1,539.0 x 456.0 = ?

When these numbers are entered into the calculator, the result is 701,784.

1,539.0 x 456.0 = 701,784

Now determine how many significant figures are in the two numbers that are multiplied together.

1,539.0 x 456.0 = 701,784

Thus, the answer can contain no more than four significant figures.

1,539.0 x 456.0 = 701,784 701,800

Notice that several zeros are added in order to maintain the same magnitude of the number.

Let´s try another example.

' + question2[index2]);