Question

Consider the calculation indicated below:

2.06 x 0.079560 x 0.20

4.070

Explain why the answer to this calculation should be reported to only two significant digits.

In multiplication/division, you line up the decimal to determine the last significant decimal place.The number of significant figures in the answer is limited by the number 0.20 which has the fewest significant figures.     The number of significant figures in the answer is the same as the first digit in the first number of the numerator, 2.06.

Answer 1

Calculations:

(2.06 x 0.079560 x 0.20)

4.070

Calculating ( 2.06 x 0.079560 x 0.20)/ 4.070

step 1: 2.06 * 0.079560 * 0.20 / 4.070

step 2: 0.1638936 * 0.20 / 4.070

step 3:  0.03277872 / 4.070

step 4:  0.0080537396

step 5: 0.0081 ( significant figures - 2, decimal places  - 4)

In doing multiplication and division only, it is good to do all calculations at once and apply the significant figures rules to the end result. And the result will contain the same number of significant figures as the quantity in the calculation having the fewest number of significant figures.

Here our result was 0.0080537396, the quantity with least significant figures is 0.20( it has two significant figures)

therefore the result will also have 2 significant figures.

Rounding off 0.0080537396 upto 2 significant places will be 0.0081( which has 2 significant figures)