Problem 63P

Correct any answers that have the incorrect number of significant figures.

(a) (3.8 × 105) − (8.45 × 105) = −4.7 × 105

(b) 0.00456 + 1.0936 = 1.10

(c) 8475.45 − 34.899 = 8440.55

(d) 908.87 − 905.34095 = 3.5291

Solution 63P

Here we have to calculate the correct number of significant figures. There are certain rules to track the significant figures from the calculated values. These are:

- For addition and subtraction, the result should contain same number of decimal places, as the measurement is carried out with the fewest decimal places.
- For multiplication and division, the result should contain same number of decimal places, as the measurement is carried out with the fewest significant figures
- Exponential terms are not considered as significant figures.
- To get the correct significant figures, we have to rounding off the figures, If the leftmost removed number is 5 or more than 5, then preceding number should be increased by .

(a) (3.8 × 105) − (8.45 × 105)

= -4.65 x 105

= −4.7 × 105

This is the correct number of significant figures. This is because 3.8 has the fewest decimal places . Exponential term is not considered as significant figures. As well as , the leftmost removed digit is more than 5, so the preceding number is increased by 1.

(b) 0.00456 + 1.0936

= 1.0981

= 1.0981

The correct number of significant figures is 1.0981. This is because 1.0936 has the fewest decimal places.

(c) 8475.45 − 34.899

= 8440.551

= 8440.55

The correct number of significant figures is 8440.55 This is because 8475.45 has two decimal places.

(d) 908.87 − 905.34095

= 3.52905

= 3.53

The correct number of significant figures is 3.53. This is because 908.87 has the lowest two decimal places. As well as the leftmost removed digit is more than 5, so the preceding number is increased by 1.