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5.1 Decimals

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By the end of this section, you will be able to:
  • Name decimals
  • Write decimals
  • Convert decimals to fractions or mixed numbers
  • Locate decimals on the number line
  • Order decimals
  • Round decimals

Before you get started, take this readiness quiz.

  1. Name the number 4,926,015 in words.
    If you missed this problem, review Introduction to Whole Numbers .
  2. Round 748 to the nearest ten.
    If you missed this problem, review Introduction to Whole Numbers .
  3. Locate 3 10 on a number line.
    If you missed this problem, review Visualize Fractions .

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 $3.45 , the bottle of water costs $1.25 , and the total sales tax is $0.33 , what is the total cost of your lunch?

A vertical addition problem is shown. The top line shows $3.45 for a sandwich, the next line shows $1.25 for water, and the last line shows $0.33 for tax. The total is shown to be $5.03.

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

Because 100 pennies = $1 , each penny is worth 1 100 of a dollar. We write the value of one penny as $0.01 , since 0.01 = 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.

Counting number Name
1 One
10 = 10 Ten
10 · 10 = 100 One hundred
10 · 10 · 10 = 1000 One thousand
10 · 10 · 10 · 10 = 10,000 Ten thousand

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

Decimal Fraction Name
0.1 1 10 One tenth
0.01 1 100 One hundredth
0.001 1 1,000 One thousandth
0.0001 1 10,000 One ten-thousandth

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 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] .

A chart is shown labeled “Place Value”. There are 12 columns. The columns are labeled, from left to right, Hundred thousands, Ten thousands, Thousands, Hundreds, Tens, Ones, Decimal Point, Tenths, Hundredths, Thousandths, Ten-thousandths, Hundred-thousandths.
This chart illustrates place values to the left and right of the decimal point.

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 $5 . 0 3 lunch? We read $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.

An image of a check is shown. The check is made out to Jane Doe. It shows the number $152.65 and says in words, “One hundred fifty two and 65 over 100 dollars.”
When we write a check, we write the amount as a decimal number as well as in words. The bank looks at the check to make sure both numbers match. This helps prevent errors.
Let’s try naming a decimal, such as 15.68.
We start by naming the number to the left of the decimal. fifteen______
We use the word “and” to indicate the decimal point. fifteen and_____
Then we name the number to the right of the decimal point as if it were a whole number. fifteen and sixty-eight_____
Last, name the decimal place of the last digit. fifteen and sixty-eight hundredths

Questions & Answers

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In economics, the contract curve refers to the set of points in an Edgeworth box diagram where both parties involved in a trade cannot be made better off without making one of them worse off. It represents the Pareto efficient allocations of goods between two individuals or entities,
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Source:  OpenStax, Prealgebra. OpenStax CNX. Jul 15, 2016 Download for free at http://legacy.cnx.org/content/col11756/1.9
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