Writing Decimals

Writing Decimals

Now we will translate the name of a decimal number into decimal notation. We will reverse the procedure we just used.

Let’s start by writing the number six and seventeen hundredths:

 six and seventeen hundredths The word and tells us to place a decimal point. ___.___ The word before and is the whole number; write it to the left of the decimal point. 6._____ The decimal part is seventeen hundredths. Mark two places to the right of the decimal point for hundredths. 6._ _ Write the numerals for seventeen in the places marked. 6.17

Example

Write fourteen and thirty-seven hundredths as a decimal.

Solution

 fourteen and thirty-seven hundredths 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. 14. _________ Mark two places to the right of the decimal point for “hundredths”. 14.__ __ Translate the words after “and” and write the number to the right of the decimal point. 14.37 Fourteen and thirty-seven hundredths is written 14.37.

How to 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.

The second bullet in Step 1 is needed for decimals that have no whole number part, like ‘nine thousandths’. We recognize them by the words that indicate the place value after the decimal – such as ‘tenths’ or ‘hundredths.’ Since there is no whole number, there is no ‘and.’ We start by placing a zero to the left of the decimal and continue by filling in the numbers to the right, as we did above.

Example

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

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.

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

$$\text{and so on…}$$

Optional Video: Write a Number in Decimal Notation from Words

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