Which of the following are exact numbers? a. There are 100 cm in 1 m. b. One meter equals 1.09

step 1 All right. So in order to do this, first what is an exact number? An exact numbers. So in some c

Which of the following are exact numbers? a. There are 100...

Which of the following are exact numbers? a. There are $100 \mathrm{~cm}$ in $1 \mathrm{~m}$. b. One meter equals $1.094$ yards. c. We can use the equation ${ }^{\circ} \mathrm{F}=\frac{9 \circ}{2} \mathrm{C}+32$ to convert from Celsius to Fahrenheit temperature. Are the numbers $\frac{9}{3}$ and 32 exact or inexact? d. $\pi=3.1415927$.

Which of the following are exact numbers?
a. There are $100 \mathrm{~cm}$ in $1 \mathrm{~m}$.
b. One meter equals $1.094$ yards.
c. We can use the equation
${ }^{\circ} \mathrm{F}=\frac{9 \circ}{2} \mathrm{C}+32$
to convert from Celsius to Fahrenheit temperature. Are the numbers $\frac{9}{3}$ and 32 exact or inexact?
d. $\pi=3.1415927$.

Key Concepts

Exact Numbers

Exact numbers are values that are known with complete precision and have no uncertainty. They usually arise from definitions, counting, or exact arithmetic operations. For example, when a conversion factor is defined by fiat (such as the exact relation between centimeters and meters), it is considered an exact number.

Inexact Numbers

Inexact numbers are approximations that result from measurements or rounded values. They carry an inherent uncertainty because they are either experimentally determined or represented with a limited number of significant figures. When numbers are approximated, they do not capture the infinite precision that is sometimes theoretically possible.

Unit Conversion Factors

Unit conversion factors are numerical relationships between different units of measure that allow for the transformation of a quantity from one unit to another. Some conversion factors are defined exactly (by international agreement or definition), while others are determined experimentally and presented as approximations with limited precision.

Mathematical Constants

Mathematical constants, such as ? (pi), have intrinsic values that often cannot be expressed exactly in decimal form because they are irrational. Any finite decimal representation of such a constant is necessarily an approximation, making it inexact despite its mathematical importance.

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