Do each of the following calculations and give the answer in...

Do each of the following calculations and give the answer in the correct units and number of significant figures:
(a) 18 pints $\times 1 \mathrm{qt} / 2$ pints;
(b) 55.0 miles per hour $\times 1.609 \mathrm{~km} / \mathrm{mile} ;$
(c) 15.45 seconds +2.2 seconds +55 seconds.

Key Concepts

Dimensional Analysis

Dimensional analysis is a method used to convert one set of units to another by using conversion factors. This technique is essential for ensuring that the units in a calculation cancel appropriately, leaving the desired units in the final answer. It is particularly useful in chemistry and physics where many equations require precise unit alignment.

Significant Figures

Significant figures refer to the digits in a number that carry meaning contributing to its measurement precision. When performing calculations, the result should be reported with the same level of precision as the least precise measurement involved. This concept helps to communicate the degree of uncertainty in a measurement and ensures that the final reported number does not imply greater precision than was present in the original data.

Arithmetic Operations on Measurements

Arithmetic operations on measurements include both multiplication and addition, each with its own rules regarding significant figures. In multiplication, the result should have the same number of significant figures as the quantity with the fewest significant figures. For addition and subtraction, the final result should be rounded to the least number of decimal places present in any of the quantities being added or subtracted. Understanding these rules is fundamental in consistently applying significant figure standards across various scientific calculations.

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