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Here you will learn about rounding decimals, including how to round to the nearest whole number, tenth, and hundredth.
Students will first learn about rounding decimals as part of number and operations in base 10 in 5th grade.
Rounding decimals involves making a decimal simpler by shortening it to a given number of decimal places. Rounding decimals is a type of estimation used to make calculations easier.
To round decimals, you can use a number line or you can apply a rule.
The rule says that if the digit to the right of the rounding digit is greater than or equal to 5 (such as, 5, 6, 7, 8, 9 ), round up by adding one to the rounding digit. However, when the digit to the right of the rounding digit is less than 5 , leave the rounding digit alone.
For example,
Round \bf{7\underline{8}.6} to the nearest whole number with a number line |
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78.6 is 0.6 from 78 and 0.4 from 79. It is closer to 79, so it rounds to 79. |
Round \bf{7\underline{8}.6} to the nearest whole number with the rule |
8 is in the rounding place, and 6 is to the right of the rounding digit. The rule says that if the number to the right of the rounding digit is greater than or equal to 5 \, (5, 6, 7, 8, 9), round up by adding one to the rounding digit. 6 is greater than 5 , so add 1 to 8, and 8 becomes 9. 7\underline{8}.6 → the nearest whole number is 79 |
Round \bf{1.\underline{6}1} to the nearest tenth with a number line |
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1.61 is 0.1 from 1.60 and 0.9 from 1.70. It is closer to 1.60, so it rounds to 1.6 . |
Round \bf{1.\underline{6}1} to the nearest whole number with the rule |
6 is in the rounding place, and 1 is to the right of the rounding digit. The rule says that if the number to the right of the rounding digit is greater than or equal to 5 \, (5, 6, 7, 8, 9), round up by adding one to the rounding digit. 1 is less than 5 , so leave the rounding digit the same. 1.\underline{6}1 → Rounded to the nearest tenth is 1.6 |
How does this relate to 5th grade math?
In order to round decimals with a number line:
In order to round decimals with the rule:
Assess math progress for the end of grade 4 and grade 5 or prepare for state assessments with these mixed topic, multiple choice questions and extended response questions!
DOWNLOAD FREEAssess math progress for the end of grade 4 and grade 5 or prepare for state assessments with these mixed topic, multiple choice questions and extended response questions!
DOWNLOAD FREERound 2,340.81 to the nearest whole number.
2,340.81 is being rounded to the nearest whole number, so the number line shows tenths.
Since 2,340.81 is 0.01 larger than 0.8, it is a little to the right of 2,304.8.
2Count to see if the number being rounded is closer to the number rounded down or up.
2,340.81 is a little less than 0.2 from 2,341.0.
2,340.81 rounded to the nearest whole number is 2,341.
**Note: Rounding decimal numbers does not mean that the answer will always have a decimal point. Notice, when rounding to the nearest whole number, a decimal point is not required.
Round 3.47 to the nearest tenth.
Create a number line with a scale one position smaller than the rounding number.
3.47 is being rounded to the nearest tenth, so the number line shows hundredths.
Count to see if the number being rounded is closer to the number rounded down or up.
3.47 is 0.3 away from 3.50.
3.47 rounded to the nearest tenth is 3.5.
Round 0.176 to the nearest hundredth.
Create a number line with a scale one position smaller than the rounding number.
0.176 is being rounded to the nearest hundredth, so the number line shows thousandths.
Count to see if the number being rounded is closer to the number rounded down or up.
0.176 is 0.04 away from 0.180.
0.176 rounded to the nearest hundredth is 0.18.
Round 33.91 to the nearest whole number.
Find the rounding place and look at the digit immediately to the right of the rounding place.
3\underline{3}.91 → 3 is in the rounded place (ones place)
3\underline{3}.91 → 9 is the digit immediately to the right of 3 (tenths place)
When that digit is 5 or greater, add 1 to the rounding digit. When it is less than 5, leave the rounding digit alone.
9 > 5 \; (6 is greater than 5), add 1 to the rounding digit, 3 will become 4.
Drop all the digits to the right of the rounded digit.
3\underline{3}.91 → drop the digits 9 and 1
Write the rounded number.
33.91 rounded to the nearest whole number is 34.
Round 2.22 to the nearest tenth.
Find the rounding place and look at the digit immediately to the right of the rounding place.
2.\underline{2}2 → 2 is in the rounded place (tenths place)
2.\underline{2}2 → 2 is the digit immediately to the right of 2 (hundredths place)
When that digit is 5 or greater, add 1 to the rounding digit. When it is less than 5, leave the rounding digit alone.
2 < 5 \; (2 is less than 5), leave the rounding digit the same.
Drop all the digits to the right of the rounded digit.
2.\underline{2}2 → drop the digits 2 in the hundredths place
Write the rounded number.
2.22 rounded to the nearest tenth is 2.2.
Round 0.075 to the nearest hundredth.
Find the rounding place and look at the digit immediately to the right of the rounding place.
0.0\underline{7}5 → 7 is in the rounded place (hundredths place)
0.0\underline{7}5 → 5 is the digit immediately to the right of 7 (thousandths place)
When that digit is 5 or greater, add 1 to the rounding digit. When it is less than 5, leave the rounding digit alone.
5 = 5 \; (5 is equal to 5), add 1 to the rounding digit, 7 will become 8.
Drop all the digits to the right of the rounded digit.
0.0\underline{7}5 → drop the digit 5
Write the rounded number.
0.075 rounded to the nearest hundredth is 0.08.
1. Which is 19.3 rounded to the nearest whole number?
19.3 is being rounded to the nearest whole number, so the number line shows tenths.
19.3 is 0.3 away from 19.0.
19.3 rounded to the nearest whole number is 19.
2. Which is 11.49 rounded to the nearest tenth?
11.49 is being rounded to the nearest tenth, so the number line shows hundredths.
11.49 is 0.01 away from 11.50.
11.49 rounded to the nearest tenth is 11.5.
3. Which is 4.934 rounded to the nearest hundredth?
4.934 is being rounded to the nearest hundredth, so the number line shows thousandths.
4.934 is 0.4 away from 4.930.
4.934 rounded to the nearest hundredth is 4.93.
4. Which is 0.49 rounded to the nearest whole number?
Find the rounding place and look at the digit immediately to the right of the rounding place.
\underline{0}.49 → 0 is in the rounded place (ones place)
\underline{0}.49 → 4 is the digit immediately to the right of 0 (tenths place)
4 < 5 \; (4 is less than 5), so the rounding digits stays the same.
\underline{0}.49 → drop the digits 4 and 9
0.49 rounded to the nearest whole number is 0.
5. Which is 2.31 rounded to the nearest tenth?
Find the rounding place and look at the digit immediately to the right of the rounding place.
2.\underline{3}1 → 3 is in the rounded place (tenths place)
2.\underline{3}1 → 1 is the digit immediately to the right of 3 (hundredths place)
1 < 5 \; (1 is less than 5), so the rounding digits stays the same.
2.\underline{3}1 → drop the digit 1
2.31 rounded to the nearest tenth is 2.3.
6. Which is 0.267 rounded to the nearest hundredth?
Find the rounding place and look at the digit immediately to the right of the rounding place.
0.2\underline{6}7 → 6 is in the rounded place (hundredths place)
0.2\underline{6}7 → 7 is the digit immediately to the right of 6 (thousandths place)
7 > 5 \; (7 is greater than 5), add 1 to the rounding digit, 6 will become 7.
0.2\underline{6}7 → drop the digit 7 in the thousandths
0.267 rounded to the nearest hundredth is 0.27.
Rounding can be considered a type of estimating. Both estimating and rounding approximate a number so it is easier to calculate or conceptualize. Estimating is the process of making a guess or calculation, whereas rounding shortens a number to a given position.
Even though 5 is directly in the middle, it was decided to use the digit 5 to round up. To help visualize this rule, think of the ten digits (0, 1, 2, 3, 4, 5, 6, 7, 8, 9 ) being divided into two groups.
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