5.1 Decimals

Name decimals

You probably already know quite a bit about decimals based on your experience with money. Suppose you buy a sandwich and a bottle of water for lunch. If the sandwich costs $\text{\$3.45}$ , the bottle of water costs $\text{\$1.25}$ , and the total sales tax is $\text{\$0.33}$ , what is the total cost of your lunch?

The total is $\text{\$5.03}.$ Suppose you pay with a $\text{\$5}$ bill and $3$ pennies. Should you wait for change? No, $\text{\$5}$ and $3$ pennies is the same as $\text{\$5.03}.$

Because $\text{100 pennies}=\text{\$1},$ each penny is worth $\frac{1}{100}$ of a dollar. We write the value of one penny as $\mathrm{\$0.01},$ since $0.01=\frac{1}{100}.$

Writing a number with a decimal is known as decimal notation. It is a way of showing parts of a whole when the whole is a power of ten. In other words, decimals are another way of writing fractions whose denominators are powers of ten. Just as the counting numbers are based on powers of ten, decimals are based on powers of ten. [link] shows the counting numbers.

How are decimals related to fractions? [link] shows the relation.

When we name a whole number, the name corresponds to the place value based on the powers of ten. In Whole Numbers , we learned to read $\mathrm{10,000}$ as ten thousand . Likewise, the names of the decimal places correspond to their fraction    values. Notice how the place value names in [link] relate to the names of the fractions from [link] .

Notice two important facts shown in [link] .

• The “th” at the end of the name means the number is a fraction. “One thousand” is a number larger than one, but “one thousandth” is a number smaller than one.
• The tenths place is the first place to the right of the decimal, but the tens place is two places to the left of the decimal.

Remember that $\text{\$5}.03$ lunch? We read $\text{\$5.03}$ as five dollars and three cents . Naming decimals (those that don’t represent money) is done in a similar way. We read the number $5.03$ as five and three hundredths .

We sometimes need to translate a number written in decimal notation into words. As shown in [link] , we write the amount on a check in both words and numbers.