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Chapter 1: Problem 29

Carry out these operations as if they were calculations of experimental results, and express each answer in the correct units and with the correct number of significant figures: (a) \(5.6792 \mathrm{~m}+0.6 \mathrm{~m}+4.33 \mathrm{~m}\) (b) \(3.70 \mathrm{~g}-2.9133 \mathrm{~g}\) (c) \(4.51 \mathrm{~cm} \times 3.6666 \mathrm{~cm}\) (d) \(\left(3 \times 10^{4} \mathrm{~g}+6.827 \mathrm{~g}\right) /\left(0.043 \mathrm{~cm}^{3}-0.021 \mathrm{~cm}^{3}\right)\)

Short Answer

Expert verified
Solutions: (a) 10.6 m, (b) 0.79 g, (c) 16.53 cm², (d) 1.6 × 10^6 g/cm³ (to 2 significant figures)

Step by step solution

01

Addition of Measurements

Add the numbers given in exercise (a) which are 5.6792 m, 0.6 m, and 4.33 m. Note that the result must not have more decimal places than the number with the least decimal places, which is 0.6 m (with 1 decimal place).
02

Subtraction of Measurements

Subtract the numbers provided in exercise (b) which are 3.70 g and 2.9133 g. Note that the result must not have more decimal places than the number with the least decimal places, which is 3.70 g (with 2 decimal places).
03

Multiplication of Measurements

Multiply the numbers given in exercise (c) which are 4.51 cm and 3.6666 cm. Note that the result must not have more significant figures than the number with the least significant figures, which is 4.51 cm (with 3 significant figures).
04

Combined Operation of Measurements

Perform the addition of 3 × 10^4 g and 6.827 g, then subtract 0.043 cm³ and 0.021 cm³ as provided in exercise (d). Finally, divide the result of the addition by the result of the subtraction. For the subtraction operation, note that the result must not have more decimal places than the number with the least decimal places, which is 0.043 cm³ (with 2 decimal places). Also, the result of the final division should not have more significant figures than the input with the least number of significant figures.

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