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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

Video Source (06:41 mins) | Transcript

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: \(97.44\)

Additional Resources

Practice Problems

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

    (Video Source | Transcript)
    )
  2. Round the number 27070 to the nearest hundred. (
    Solution
    x
    Solution: 27100
    Details:
    Image shows a box with the number 27070 above each digit, a diagonal box across the top shows the name of each corresponding place value.
    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.

    Image shows the number line from zero to ten with number 7 highlighted in red.
    After increasing the 0 to 1 in the hundreds place, turn all the numbers to the right of the hundreds place into zeros.
    \(27,{\color{red}1}00\)

    The rounded answer is 27100.
    )
  3. Round the number 47397686 to the nearest million. (
    Solution
    x
    Solution: 47000000
    Details:
    Image shows a box with the number 47397686. This image shows the number 47,397,686 and the names of the place values of each digit written above them. Starting on the left and going right, the 4 is in the ten millions place. The 7 is in the millions place. The 3 is in the hundred thousands place. The 9 i in the ten thousands place. The 7 is in the thousands place. The 6 is in the hundreds place. The 8 is in the tens place. The last 6 is in the ones place.

    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.

    Image shows a number line from zero to ten with three highlighted in red.

    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.
    \(4{\color{red} 7}000000\)

    The rounded answer is 47,000,000.
    )
  4. Round the number 0.62968 to the nearest hundredth. (
    Solution
    x
    Solution:
    0.63
    )
  5. Round the number 856.861203 to the nearest thousandth. (
    Solution
    x
    Solution:
    856.861
    )
  6. Round the number 599.495 to the nearest tenth. (
    Video Solution
    x
    Solution: 599.5
    Details:

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

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