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Round a Number to a Specified Precision
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We may get an answer that has a very long list of decimals, like 3.1415926535897932… We don’t want to have to write that all of the time, but ending it early causes us to lose some precision. 3 is not the same as 3.14, which is not the same as 3.1415. Precision is the number of decimal places you keep on the number. The more you keep, the closer your number is to the correct number. In many problems you’ll be solving in future lessons, you’ll be asked to round your answer to a certain precision.

Rounding to any place value

Remember, when rounding, look at the digit to the right of the place value you want to round to (if you’re rounding to the tenths place, look at the hundredths place), if it’s less than or equal to 4 the place value you are rounding to stays the same. If the place value to the right is greater than or equal to 5, add 1 to the place value you are rounding to.

Place Value to the Right How to Round to a Specific Place Value Example
0,1,2,3,4 Keep the number in the place value you are rounding to the same.

Round $$-17.43$$ to nearest tenth: $$-17.4$$

Round $$97.432$$ to the nearest hundredth: $$97.43$$

5,6,7,8,9 Increase the number in the place value you are rounding to by 1.

Round $$12.59$$ to the nearest tenth: $$12.6$$

Round $$97.436$$ to the nearest hundredth: $$97.44$$

### Practice Problems

1. Round the number 227.18 to the nearest ten. (
Video Solution
Solution: 230
Details:

(Video Source | Transcript)
)
2. Round the number 27070 to the nearest hundred. (
Solution
Solution: 27100
Details: The zero is in the hundreds place.
$$27,{\color{red}0}70$$

To the right of 0 is the number 7.
$$27,{\color{red}0}{\color{green}7}0$$

To determine if 0 is to be increased, look at the position of the number 7 on the number line. Since the number 7 is higher than 5, we will increase 0 by 1 which is 1. After increasing the 0 to 1 in the hundreds place, turn all the numbers to the right of the hundreds place into zeros.
$$27,{\color{red}1}00$$

)
3. Round the number 47397686 to the nearest million. (
Solution
Solution: 47000000
Details: Look at the 7 in the millions place.
$$4{\color{red} 7}397686$$

To determine if 7 is to be increased by one or stay the same, look at the number on the right.
To the right of 7 is the number 3.
$$4{\color{red} 7}{\color{green} 3}97686$$

The number 3 is less than 5, so the number 7 will not increase and will just stay the same. After determining that the number 7 in the millions place will not change, turn all the numbers to the right of the 7 into zeros.
$$4{\color{red} 7}000000$$

)
4. Round the number 0.62968 to the nearest hundredth. (
Solution
Solution:
0.63
)
5. Round the number 856.861203 to the nearest thousandth. (
Solution
Solution:
856.861
)
6. Round the number 599.495 to the nearest tenth. (
Video Solution
Solution: 599.5
Details:

(Video Source |Transcript)
)
7. Round the number 599.995 to the nearest tenth. (
Solution
Solution:
600
)

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