Problem 61P

Perform each calculation to the correct number of significant figures.

(a) 87.6 + 9.888 + 2.3 + 10.77

(b) 43.7 − 2.341

(c) 89.6 + 98.33 − 4.674

(d) 6.99 − 5.772

Solution 61P

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.

(a) 87.6 + 9.888 + 2.3 + 10.77

Here, addition operation is carried out

= 110.558

= 110.6

Thus, (a) have four significant figures. Because 2.3 has the fewest ( one) decimal place. Thus correct number of significant figures of (a) is 110.6

(b) 43.7 − 2.341

Here, subtraction operation is carried out

= 41.359

= 41.4

(rounding off to three significant figures as it contains 43.7 which have only one decimal places. As well as, the leftmost removed digit is 5, so the preceding number is increased by 1)

Therefore , 3 significant figures are there in(b)

Thus correct number of significant figures of (b) is 41.4

(c) 89.6 + 98.33 − 4.674

= 187.93 - 4.674 = 183.256

= 183.3

(rounding off to four significant figures, because the operation contains lowest 89.6 which have the fewest (one) decimal places.)

Therefore , 4 significant figures are there in(C)

Thus correct number of significant figures of (C) is 183.3

(d) 6.99 − 5.772

= 1.218

= 1.22

(rounding off to three significant figures , because the operation contains 6.99 which have the lowest two decimal places)

As well as, the leftmost removed digit is more than 5, so the preceding number is increased by 1)

Therefore , 3 significant figures are there in(d)

Thus correct number of significant figures of (d) is 1.22