1.7 Decimals

Elementary algebra Page 1 / 10

By the end of this section, you will be able to:

Name and write decimals
Round decimals
Add and subtract decimals
Multiply and divide decimals
Convert decimals, fractions, and percents

A more thorough introduction to the topics covered in this section can be found in the Prealgebra chapter, Decimals .

Name and write decimals

Decimals are another way of writing fraction s whose denominators are powers of 10.

\begin{matrix} 0.1 & = & \frac{1}{10} & 0.1 is “one tenth” \\ 0.01 & = & \frac{1}{100} & 0.01 is “one hundredth” \\ 0.001 & = & \frac{1}{1,000} & 0.001 is “one thousandth” \\ 0.0001 & = & \frac{1}{10,000} & 0.0001 is “one ten-thousandth” \end{matrix}

Notice that “ten thousand” is a number larger than one, but “one ten-thousand th ” is a number smaller than one. The “th” at the end of the name tells you that the number is smaller than one.

When we name a whole number, the name corresponds to the place value based on the powers of ten. We read 10,000 as “ten thousand” and 10,000,000 as “ten million.” Likewise, the names of the decimal places correspond to their fraction values. [link] shows the names of the place values to the left and right of the decimal point.

A table is shown with the title Place Value. From left to right the row reads “Hundred thousands,” “Ten thousands,” “Thousands,” “Hundreds,” “Tens,” and “Ones.” Then there is a blank cell and below it is a decimal point. To the right of this, the cells read “Tenths,” “Hundredths,” “Thousandths,” “Ten-thousandths,” and “Hundred-thousandths.” — Place value of decimal numbers are shown to the left and right of the decimal point.

How to name decimals

Name the decimal 4.3.

Solution

A table is given with four steps. Additionally, the number 4.3 is given. The first step reads “Step 1. Name the number to the left of the decimal point.” To the right of this, it is noted that “4 is to the left of the decimal point.” To the right of this, it reads “four” followed by a large blank space.

The second step reads “Step 2. Write ‘and’ for the decimal point.” To the right of this it reads “four and” followed by a blank space.

The third step reads “Step 3. Name the ‘number’ part to the right of the decimal point as if it were a whole number.” To the right of this, it reads “3 is to the right of the decimal point.” To the right of this, it reads “four and three” followed by a blank.

Finally, the last step reads “Step 4. Name the decimal place.” To the right of this, it reads “four and three tenths.”

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Name the decimal: $6.7 .$

six and seven tenths

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Name the decimal: $5.8 .$

five and eight tenths

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We summarize the steps needed to name a decimal below.

Name a decimal.

Name the number to the left of the decimal point.
Write “and” for the decimal point.
Name the “number” part to the right of the decimal point as if it were a whole number.
Name the decimal place of the last digit.

Name the decimal: $−15.571 .$

Solution

$\begin{matrix} −15.571 \\ Name the number to the left of the decimal point. & negative fifteen __________________________________ \\ Write “and” for the decimal point. & negative fifteen and ______________________________ \\ Name the number to the right of the decimal point. & negative fifteen and five hundred seventy-one __________ \\ The 1 is in the thousandths place. & negative fifteen and five hundred seventy-one thousandths \end{matrix}$

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Name the decimal: $−13.461 .$

negative thirteen and four hundred sixty-one thousandths

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Name the decimal: $−2.053 .$

negative two and fifty-three thousandths

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When we write a check we write both the numerals and the name of the number. Let’s see how to write the decimal from the name.

How to write decimals

Write “fourteen and twenty-four thousandths” as a decimal.

Solution

A table is given with four steps. The first step reads “Step 1. Look for the work ‘and’ – it locates the decimal point. Place a decimal point under the word ‘and’. Translate the words before ‘and’ into the whole number and place it to the left of the decimal point.” To the right of this, we have the words “fourteen and twenty-four thousandths.” Below this word, we have “fourteen and twenty-four thousandths” with the word “and” underlined. Below this word, we have a small blank space separated from a larger blank space by a decimal point. Under this, we have 14 in the small blank space followed by the decimal point and the larger blank space.

The second step reads “Step 2. Mark the number of decimal places needed to the right of the decimal point by noting the place value indicated by the last word.” To the right of this it reads “The last word is thousandths.” To the right of this there is the number 14 followed by a decimal point and three small blank spaces. Under the blank spaces, the words “tenths,” “hundredths,” and “thousandths” are written.

The third step reads “Step 3. Translate the words after ‘and’ into the number to the right of the decimal point. Write the number in the spaces – putting the final digit in the last place.” To the right of this, we have 14 followed by a decimal followed by a blank space followed by 2 and 4 on the other two previously blank spaces.

Finally, the last step reads “Step 4. Fill in zeros for empty place holders as needed.” To the right of this, it reads “Zeros are needed in the tenths place.” To the right of this, we have 14 followed by a decimal point followed by 0, 2, and 4, respectively, on the blank spaces. Below this, we have “fourteen and twenty-four thousandths is written 14.024.”

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Write as a decimal: thirteen and sixty-eight thousandths.

13.68

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Write as a decimal: five and ninety-four thousandths.

5.94

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We summarize the steps to writing a decimal .

Write a decimal.

Look for the word “and”—it locates the decimal point.
- Place a decimal point under the word “and.” Translate the words before “and” into the whole number and place it to the left of the decimal point.
- If there is no “and,” write a “0” with a decimal point to its right.
Mark the number of decimal places needed to the right of the decimal point by noting the place value indicated by the last word.
Translate the words after “and” into the number to the right of the decimal point. Write the number in the spaces—putting the final digit in the last place.
Fill in zeros for place holders as needed.

Questions & Answers

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Source: OpenStax, Elementary algebra. OpenStax CNX. Jan 18, 2017 Download for free at http://cnx.org/content/col12116/1.2

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