5.1 Decimals  (Page 3/8)

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Write a decimal number from its name.

1. Look for the word “and”—it locates the decimal point.
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.
• 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.
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.
4. Fill in zeros for place holders as needed.

If there is no whole number, we write a 0 to the left of the decimal point as a placeholder. So we would write "nine tenths" as 0.9.

Write twenty-four thousandths as a decimal.

Solution

 twenty-four thousandths Look for the word "and". There is no "and" so start with 0 0. To the right of the decimal point, put three decimal places for thousandths. Write the number 24 with the 4 in the thousandths place. Put zeros as placeholders in the remaining decimal places. 0.024 So, twenty-four thousandths is written 0.024

Write as a decimal: fifty-eight thousandths.

0.058

Write as a decimal: sixty-seven thousandths.

0.067

Before we move on to our next objective, think about money again. We know that $\text{1}$ is the same as $\text{1.00}.$ The way we write $\text{1}\phantom{\rule{0.2em}{0ex}}\left(\text{or}\phantom{\rule{0.2em}{0ex}}\text{1.00}\right)$ depends on the context. In the same way, integers can be written as decimals with as many zeros as needed to the right of the decimal.

$\begin{array}{cccc}5=5.0\hfill & & & -2=-2.0\hfill \\ 5=5.00\hfill & & & -2=-2.00\hfill \\ 5=5.000\hfill & & & -2=-2.000\hfill \end{array}$
$\text{and so on…}$

Convert decimals to fractions or mixed numbers

We often need to rewrite decimals as fractions or mixed numbers. Let’s go back to our lunch order to see how we can convert decimal numbers to fractions. We know that $\text{5.03}$ means $5$ dollars and $3$ cents. Since there are $100$ cents in one dollar, $3$ cents means $\frac{3}{100}$ of a dollar, so $0.03=\frac{3}{100}.$

We convert decimals to fractions by identifying the place value of the farthest right digit. In the decimal $0.03,$ the $3$ is in the hundredths place, so $100$ is the denominator of the fraction equivalent to $0.03.$

$0.03=\frac{3}{100}$

For our $\text{5.03}$ lunch, we can write the decimal $5.03$ as a mixed number.

$5.03=5\frac{3}{100}$

Notice that when the number to the left of the decimal is zero, we get a proper fraction. When the number to the left of the decimal is not zero, we get a mixed number.

Convert a decimal number to a fraction or mixed number.

1. Look at the number to the left of the decimal.
• If it is zero, the decimal converts to a proper fraction.
• If it is not zero, the decimal converts to a mixed number.
• Write the whole number.
2. Determine the place value of the final digit.
3. Write the fraction.
• numerator—the ‘numbers’ to the right of the decimal point
• denominator—the place value corresponding to the final digit
4. Simplify the fraction, if possible.

Write each of the following decimal numbers as a fraction or a mixed number:

$\phantom{\rule{0.2em}{0ex}}4.09$ $\phantom{\rule{0.2em}{0ex}}3.7$ $\phantom{\rule{0.2em}{0ex}}-0.286$

Solution

 ⓐ 4.09 There is a 4 to the left of the decimal point. Write "4" as the whole number part of the mixed number. Determine the place value of the final digit. Write the fraction. Write 9 in the numerator as it is the number to the right of the decimal point. Write 100 in the denominator as the place value of the final digit, 9, is hundredth. The fraction is in simplest form.

Did you notice that the number of zeros in the denominator is the same as the number of decimal places?

 ⓑ 3.7 There is a 3 to the left of the decimal point. Write "3" as the whole number part of the mixed number. Determine the place value of the final digit. Write the fraction. Write 7 in the numerator as it is the number to the right of the decimal point. Write 10 in the denominator as the place value of the final digit, 7, is tenths. The fraction is in simplest form.

 ⓒ −0.286 There is a 0 to the left of the decimal point. Write a negative sign before the fraction. Determine the place value of the final digit and write it in the denominator. Write the fraction. Write 286 in the numerator as it is the number to the right of the decimal point. Write 1,000 in the denominator as the place value of the final digit, 6, is thousandths. We remove a common factor of 2 to simplify the fraction.

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