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# Introduction to Decimals Study Guide (page 3)

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## Rounding Decimals

Rounding a decimal is a means of estimating its value using fewer digits. To find an answer more quickly, especially if you don't need an exact answer, you can round each decimal to the nearest whole number before doing the arithmetic. For example, you could use rounding to approximate the sum of 3.456789 and 16.738532:

Since 3.456789 is closer to 3 than it is to 4, it can be rounded down to 3, the nearest whole number. Similarly,16.738532 is closer to 17 than it is to 16, so it can be rounded up to 17, the nearest whole number.

Rounding may also be used to simplify a single figure, like the answer to some arithmetic operation. For example, if your investment yielded \$14,837,812.98 (wishful thinking!), you could simplify it as approximately \$15 million, rounding it to the nearest million dollars.

Rounding is a good way to do a reasonableness check on the answer to a decimal arithmetic problem: Estimate the answer to a decimal arithmetic problem and compare it to the actual answer to be sure it's in the ballpark.

## Rounding to the Nearest Whole Number

To round a decimal to the nearest whole number, look at the decimal digit to the right of the whole number, the tenths digit, and follow these guidelines:

• If the digit is less than 5,round down by dropping the decimal point and all the decimal digits. The whole number portion remains the same.
• If the digit is 5 or more, round up to the next larger whole number.

Examples of rounding to the nearest whole number:

• 25.3999 rounds down to 25 because 3 is less than 5.
• 23.5 rounds up to 24 because the tenths digit is 5.
• 2.613 rounds up to 3 because 6 is greater than 5.

## Rounding to the Nearest Tenth

Decimals can be rounded to the nearest tenth in a similar fashion. Look at the digit to its right, the hundredths digit, and follow these guidelines:

• If the digit is less than 5, round down by dropping that digit and all the decimal digits following it.
• If the digit is 5 or more, round up by making the tenths digit one greater and dropping all the digits to its right.

Examples of rounding to the nearest tenth:

• 45.32 rounds down to 45.3 because 2 is less than 5.
• 33.15 rounds up to 33.2 because the hundredths digit is 5.
• \$14,837,812 rounds down to \$14.8 million, the nearest tenth of a million dollars, because 3 is less than 5.
• 2.96 rounds up to 3.0 because 6 is greater than 5. Notice that you cannot simply make the tenths digit, 9, one greater—that would make it 10. Therefore, the 9 becomes a zero and the whole number becomes one greater.

Similarly, decimals can be rounded to the nearest hundredth, thousandth, and so forth by looking at the next decimal digit to the right:

• If it's less than 5, round down.
• If it's 5 or more, round up.

#### Tip

Remember, when rounding to the nearest tenth, you are actually looking at the hundredth place to see if you need to round down or up. It works the same way with other rounding: when rounding to the nearest hundredth, you must look at the thousandth place to determine the rounding. When rounding to the nearest thousandth, you must look at the ten-thousandth place.

#### Tip

As you pay for things throughout the day, take a look at the prices. Are they written in dollars and cents? If so, how would you read the numbers aloud using the terms discussed in this lesson? For a bit of a challenge, insert a zero in the tenths column of the number, thereby pushing the two numbers right of the decimal place one place to the right. Now how would you say the amount out loud? Learning how to correctly express decimals verbally will show others how math-savvy you are!

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