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# Decimal Word Problems Study Guide

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## Introduction to Decimal Word Problems

How many times can you subtract 7 from 83, and what is left afterwards? You can subtract it as many times as you want, and it leaves 76 every time.

—AUTHOR UNKNOWN

Certain situations can seem complicated, but underneath, they are really not that difficult. This lesson will focus on the basics of decimals and decimal word problems, so that they will not seem as difficult the next time around.

### Decimal Place Value

Decimals are based on place value. Each place value is named by the distance it is from the decimal point. Commonly used decimal places are shown in the following figure.

#### Tip:

Remember, decimals and fractions are very closely related. Take these examples:

The decimal 0.3, which is three tenths, is equal to.
The decimal 0.21, which is twenty-one hundredths, is equal to .
The decimal 0.127, which is one hundred twenty-seventhousandths, is equal to .

## Rounding Decimals

To round a decimal to a certain place value, look to the decimal place to the right of the place that you are rounding. If the digit to the right is 4 or less, keep the number in the place value and drop the numbers to the right. For example, to round the number 2.354 to the nearest hundredth, look to the number 4 in the thousandths place. Because this number is 4 or less, keep the 5 in the hundredths place and drop the digit to the right. The rounded decimal becomes 2.35.

To round the number 6.178 to the nearest tenth, look to the 7 in the hundredths place. Because this number is 5 or greater, round the 1 in the tenths place to 2 and drop the digits to the right. The rounded number becomes 6.2.

#### Tip:

Remember that our money system is based on dollars and cents. When rounding with money, always round to the nearest hundredth, unless told otherwise.

To add or subtract decimals, line up the decimal points and then add or subtract as you would whole numbers. For example, to add 12.26 + 14.11, line up the decimal points vertically and add.

#### Tip:

When you are adding or subtracting, if one number goes out more decimal places than another, trailing zeros can be added to the right of the decimal point to make the problem easier. For example, when adding 2.3 and 4.15 you may line up the numbers as follows and add a zero after the 3 in 2.3:

As always, be sure to line up the decimal points when adding and subtracting.

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