Rounding Whole Numbers

Rounding Whole Numbers

Learning Objective(s)

· Learn the rules for rounding.

· Round whole numbers to specific place values, including tens, hundreds, and thousands.

Introduction

In some situations, you don’t need an exact answer. In these cases, rounding the number to a specific place value is possible. For example, if you travelled 973 miles, you might want to round the distance to 1,000 miles, which is easier to think about. Rounding also comes in handy to see if a calculation is reasonable.

Rounding Whole Numbers

These are the rules for rounding whole numbers:

First, identify the digit with the place value to which you are rounding. You might circle or highlight the digit so you can focus on it better.

Then, determine the possible numbers that you would obtain by rounding. These possible numbers are close to the number that you’re rounding to, but have zeros in the digits to the right.

If you are rounding 186 to the nearest ten, then180 and 190 are the two possible numbers to round to, as 186 is between 180 and 190. But how do you know whether to round to180 or 190?

Usually, round a number to the number that is closest to the original number.

When a number is halfway between the two possible numbers, round up to the greater number.

Since 186 is between 180 and 190, and 186 is closer to 190, you round up to 190.

You can use a number line to help you round numbers.

Example
Problem	A camera is dropped out of a boat, and sinks to the bottom of a pond that is 37 feet deep. Round 37 to the nearest ten.
37		The digit you’re rounding to is the tens digit, 3.
30 37 40		37 is between 30 and 40.
$C:\Documents and Settings\nkatz\Desktop\NROC\Geogebra\U01_L1_T2_text_images\U01_L1_T2_text_image7.png$		37 is only 3 away from 40, but it’s 7 away from 30. So, 37 is closer to 40.
Answer To the nearest ten, 37 rounds to 40.

Example
Problem		Round 33 to the nearest ten.
$C:\Documents and Settings\nkatz\Desktop\NROC\Geogebra\U01_L1_T2_text_images\U01_L1_T2_text_image8.png$ 33 30, because 33 is closer to 30.
Answer	To the nearest ten, 33 rounds to 30.

You can determine where to round without using a number line by looking at the digit to the right of the one you’re rounding to. If that digit is less than 5, round down. If it’s 5 or greater, round up. In the example above, you can see without a number line that 33 is rounded to 30 because the ones digit, 3, is less than 5.

*Example*
Problem		*Round 77 to the nearest ten.*
77 80, because the ones digit, 7, is 5 or greater.
Answer	77 rounded to the nearest ten is 80.

Example
Problem		There are 576 jellybeans in a jar. Round this number to the nearest ten.
576 580, because the ones digit, 6, is 5 or greater.
Answer	576 rounded to the nearest ten is 580.

In the previous examples, you rounded to the tens place. The rounded numbers had a 0 in the ones place. If you round to the nearest hundred, the rounded number will have zeros in the tens and ones places. The rounded number will resemble 100, 500, or 1200.

Example
Problem		A runner ran 1,539 meters, but describes the distance he ran with a rounded number. Round 1,539 to the nearest hundred.
1,539 1,500, because the next digit is less than 5.
Answer	1,539 rounded to the nearest hundred is 1,500.

If you round to the nearest thousand, the rounded number will have zeros in the hundreds, tens, and ones places. The rounded number will resemble 1,000, 2,000, or 14,000.

Example
Problem	A plane’s altitude increased by 2,721 feet. Round this number to the nearest thousand.
2,721 3,000, because the next digit, 7, is 5 or greater.
Answer 2,721 rounded to the nearest thousand is 3,000.

Now that you know how to round to the nearest ten, hundred, and thousand, try rounding to the nearest ten thousand.

Example
Problem		Round 326,749 to the nearest ten thousand.
326,749 330,000, because the next digit, 6, is 5 or greater.
Answer	326,749 rounded to the nearest ten thousand is 330,000.

A record number of 23,386 people voted in a city election. Round this number to the nearest hundred.

A) 23,300

B) 23,400

C) 23,000

D) 23,390

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Summary

In situations when you don’t need an exact answer, you can round numbers. When you round numbers, you are always rounding to a particular place value, such as the nearest thousand or the nearest ten. Whether you round up or round down usually depends on which number is closest to your original number. When a number is halfway between the two possible numbers, round up to the larger number.