1.7 Decimals  (Page 5/10)

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 $\frac{374}{\mathrm{1,000}}$ is the same as the number of decimal places in 0.374?

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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 $4÷5$ or $5\overline{)4}.$ This leads to the following method for converting a fraction to a decimal.

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

Solution

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

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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.

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

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

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.

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

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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