1.7 Decimals (Page 5/10)

Elementary algebra Page 5 / 10

Convert a decimal to a proper fraction.

Determine the place value of the final digit.
Write the fraction.
- numerator—the “numbers” to the right of the decimal point
- denominator—the place value corresponding to the final digit

Write 0.374 as a fraction.

Solution

	$0.374$
Determine the place value of the final digit.
Write the fraction for 0.374: The numerator is 374. The denominator is 1,000.	$\frac{374}{1000}$
Simplify the fraction.	$\frac{2 \cdot 187}{2 \cdot 500}$
Divide out the common factors.	$\frac{187}{500}$ so, $0.374 = \frac{187}{500}$

Did you notice that the number of zeros in the denominator of $\frac{374}{1,000}$ is the same as the number of decimal places in 0.374?

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Write 0.234 as a fraction.

$\frac{117}{500}$

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Write 0.024 as a fraction.

$\frac{3}{125}$

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We’ve learned to convert decimals to fractions. Now we will do the reverse—convert fractions to decimals. Remember that the fraction bar means division. So $\frac{4}{5}$ can be written $4 \div 5$ or $54 .$ This leads to the following method for converting a fraction to a decimal.

Convert a fraction to a decimal.

To convert a fraction to a decimal, divide the numerator of the fraction by the denominator of the fraction.

Write $- \frac{5}{8}$ as a decimal.

Solution

Since a fraction bar means division, we begin by writing $\frac{5}{8}$ as $85 .$ Now divide.

This is a long division problem with 8 dividing 5.000 and 0.625 as the quotient. Below 5.000 we have 48, a solid horizontal line, 20, 16, a solid horizontal line, 40, 40, and a final horizontal line. So five eighths equals 0.625.

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Write $- \frac{7}{8}$ as a decimal.

$−0.875$

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Write $- \frac{3}{8}$ as a decimal.

$−0.375$

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When we divide, we will not always get a zero remainder. Sometimes the quotient ends up with a decimal that repeats. A repeating decimal is a decimal in which the last digit or group of digits repeats endlessly. A bar is placed over the repeating block of digits to indicate it repeats.

Repeating decimal

A repeating decimal is a decimal in which the last digit or group of digits repeats endlessly.

A bar is placed over the repeating block of digits to indicate it repeats.

Write $\frac{43}{22}$ as a decimal.

Solution

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Write $\frac{27}{11}$ as a decimal.

$2. \overset{—}{45}$

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Write $\frac{51}{22}$ as a decimal.

$2.3 \overset{—}{18}$

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Sometimes we may have to simplify expressions with fractions and decimals together.

Simplify: $\frac{7}{8} + 6.4 .$

Solution

First we must change one number so both numbers are in the same form. We can change the fraction to a decimal, or change the decimal to a fraction. Usually it is easier to change the fraction to a decimal.

		$\frac{7}{8} + 6.4$
Change $\frac{7}{8}$ to a decimal.
Add.		$0.875 + 6.4$
		$7.275$
		So, $\frac{7}{8} + 6.4 = 7.275$

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Simplify: $\frac{3}{8} + 4.9 .$

5.275

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Simplify: $5.7 + \frac{13}{20} .$

6.35

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A percent is a ratio whose denominator is 100. Percent means per hundred. We use the percent symbol, %, to show percent.

Percent

A percent is a ratio whose denominator is 100.

Since a percent is a ratio, it can easily be expressed as a fraction. Percent means per 100, so the denominator of the fraction is 100. We then change the fraction to a decimal by dividing the numerator by the denominator.

\begin{matrix} 6% & 78% & 135% \\ Write as a ratio with denominator 100 . & \frac{6}{100} & \frac{78}{100} & \frac{135}{100} \\ Change the fraction to a decimal by dividing & 0.06 & 0.78 & 1.35 \\ the numerator by the denominator. \end{matrix}

Do you see the pattern? To convert a percent number to a decimal number, we move the decimal point two places to the left.

The first part of this figure shows 6% with an arrow drawn from between the 6 and the percentage sign to the space to the left of 6 and then to the space further to the left of that space. Below this, the number 0.06 is given. The second part of this figure shows 78% with an arrow drawn from between the 8 and the percentage sign to the space between the 7 and the 8 and then to the space to the left of the 7. Below this, the number 0.78 is given. The third part of this figure shows 2.7% with an arrow drawn from the decimal point to the space to the left of the 2 and then to the space further to the left of that space. Below this, the number 0.027 is given. The fourth part of this figure shows 135% with an arrow drawn from between the 5 and the percentage sign to the space between 3 and 5 and then to the space between 1 and 3. Below this, the number 1.35 is given.

Convert each percent to a decimal: ⓐ 62% ⓑ 135% ⓒ 35.7%.

Solution

ⓐ

Move the decimal point two places to the left.	$0.62$

ⓑ

Move the decimal point two places to the left.	$1.35$

ⓒ

Move the decimal point two places to the left.	$0.057$

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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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