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Chapter 1: Problem 31

Which of the following are exact numbers? a. There are 100 cm in 1 m. b. One meter equals 1.094 yards. c. We can use the equation $$^\circ \mathrm{F}=\frac{9}{5}^{\circ} \mathrm{C}+32$$ to convert from Celsius to Fahrenheit temperature. Are the numbers \(\frac{9}{5}\) and 32 exact or inexact? d. \(\pi=3.1415927\)

Short Answer

Expert verified
a. Exact b. Inexact c. Exact (both \(\frac{9}{5}\) and 32) d. Inexact

Step by step solution

01

Statement a: 100 cm in 1 m

This statement tells us there are exactly 100 centimeters in one meter. Since this is a precise and definite value, the number 100 is an exact number in this case.
02

Statement b: One meter equals 1.094 yards

This statement provides a conversion factor between meters and yards. The number 1.094 is a rounded version of the actual conversion factor, and therefore, it is an inexact number.
03

Statement c: Celsius to Fahrenheit conversion equation

The Celsius-to-Fahrenheit conversion equation is given as: \[^{\circ} \mathrm{F}=\frac{9}{5}^{\circ} \mathrm{C}+32\] In this equation, both the fraction \(\frac{9}{5}\) and the number 32 are used as exact conversion constants. Therefore, both numbers are exact in this case.
04

Statement d: \(\pi = 3.1415927\)

The value of pi in this statement is given as 3.1415927. We know that the actual value of \(\pi\) cannot be accurately represented by a finite decimal or simple fraction. Therefore, the number 3.1415927 is an inexact representation of \(\pi\).

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Most popular questions from this chapter

Consider multiplying 26.2 by 16.43. What would a mathematician say the answer is? What would a scientist say? Justify the scientist’s answer, not merely citing the rule, but explaining it.

Perform the following mathematical operations, and express the result to the correct number of significant figures. a. \(\frac{2.526}{3.1}+\frac{0.470}{0.623}+\frac{80.705}{0.4326}\) b. \((6.404 \times 2.91) /(18.7-17.1)\) c. \(6.071 \times 10^{-5}-8.2 \times 10^{-6}-0.521 \times 10^{-4}\) d. $\left(3.8 \times 10^{-12}+4.0 \times 10^{-13}\right) /\left(4 \times 10^{12}+6.3 \times 10^{13}\right)$ e. \(\frac{9.5+4.1+2.8+3.175}{4}\) (Assume that this operation is taking the average of four numbers. Thus 4 in the denominator is exact.) f. \(\frac{8.925-8.905}{8.925} \times 100\) (This type of calculation is done many times in calculating a percentage error. Assume that this example is such a calculation; thus 100 can be considered to be an exact number.)

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