Problem 65P

Perform each calculation to the correct number of significant figures.

(a) (78.4 − 44.889) ÷ 0.0087

(b) (34.6784 × 5.38) + 445.56

(c) (78.7 × 105 ÷ 88.529) + 356.99

(d) (892 ÷ 986.7) + 5.44

Problem 65P

Perform each calculation to the correct number of significant figures.

(a) (78.4 − 44.889) ÷ 0.0087

(b) (34.6784 × 5.38) + 445.56

(c) (78.7 × 105 ÷ 88.529) + 356.99

(d) (892 ÷ 986.7) + 5.44

Solution: Here, we are going to perform the given calculations to the correct number of significant figures.

Step1:

When addition or subtraction is carried out in the numbers having different precisions, the final result should be reported up to the same number of decimal places as are present in the term having the least number of decimal places.

Again, in multiplication or division, the final result should be reported up to the same number of significant numbers as are present in the term with the least number of significant figures.

Step2:

a) (78.4 - 44.889) 0.0087

The first two numbers are to be operated first as follows:

78.4 - 44.889 = 33.511 = 33.5(rounded off to one decimal place)

Since 78.4 contains digits up to one decimal place, therefore, the answer must be reported/ rounded off up to one decimal place.

Upon further division, the final result can be calculated as :

33.5 0.0087 = 3850.57 = 3900(rounded off up to two significant figures. )

b) (34.6784 x 5.38) + 445.56

The first two numbers are to be operated first as follows:

34.6784 x 5.38 = 186.569792 = 186(rounded off to three significant numbers)

Upon further addition, the final result can be calculated as :

186 + 445.56 = 631.56 = 631(rounded off up to zero decimal places)

c) (78.7 × 105 ÷ 88.529) + 356.99

The first three numbers are to be operated first as follows:

78.7 × 105 ÷ 88.529 = 93.34229 = 93.3(rounded off to three significant numbers)

Upon further addition, the final result can be calculated as :

93.3 + 356.99 = 450.29 = 450.3(rounded off up to one decimal place)

d) (892 ÷ 986.7) + 5.44

The first two numbers are to be operated first as follows:

892 ÷ 986.7 = 0.90402 = 0.904(rounded off to three significant numbers)

Upon further addition, the final result can be calculated as :

0.904 + 5.44 = 6.344 = 6.34(rounded off up to two decimal places)

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