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5th Grade · 5.NBT.A.4

Rounding decimals in 5th grade

Rounding decimals means replacing a decimal with a nearby number that is easier to work with, such as 3.7 instead of 3.68. In 5th grade, your child learns to round decimals to any place: the nearest whole number, tenth, hundredth or thousandth. The rule rests on place value, so your child should be able to explain why a number rounds up or down.

What the standard says

The official Common Core wording, quoted exactly. The plain version follows.

5.NBT.A.4 Use place value understanding to round decimals to any place.

What it means, in plain words

A decimal has digits to the right of the decimal point. The first is the tenths place, the next is the hundredths place and the third is the thousandths place. In 4.725, the 7 means 7 tenths, the 2 means 2 hundredths and the 5 means 5 thousandths.

To round, your child finds the digit in the place the question names. Then the child looks at the one digit just to its right. If that digit is 5 or more, the rounding digit goes up by one. If it is less than 5, the rounding digit stays the same. The digits after the rounding place are dropped.

Rounding decimals to the nearest tenth and rounding decimals to the nearest hundredth are the most common tasks. A number line shows why the rule works. The number 2.63 sits between 2.6 and 2.7, and it is closer to 2.6, so it rounds to 2.6. Halfway between them is 2.65, and from there numbers round up.

Your child should be able to:

  • Name the tenths, hundredths and thousandths places in a decimal
  • Round a decimal to the nearest whole number, tenth, hundredth or thousandth
  • Show on a number line why a decimal rounds up or down
  • Use rounded numbers to estimate a sum or a product

Example

Round 7.382 to the nearest tenth.

  1. The tenths digit is 3, so the answer is either 7.3 or 7.4.
  2. Look at the next digit to the right, the hundredths digit. It is 8.
  3. 8 is 5 or more, so the 3 goes up to 4 and the digits after it are dropped.
  4. 7.382 rounded to the nearest tenth is 7.4.

Example

Round 8.635 to the nearest hundredth.

  1. The hundredths digit is 3, so the answer is either 8.63 or 8.64.
  2. The next digit to the right, the thousandths digit, is 5.
  3. 5 counts as "5 or more", so the 3 goes up to 4.
  4. 8.635 rounded to the nearest hundredth is 8.64.

Where children usually get stuck

  • Asked to round 2.348 to the nearest tenth, your child writes 2.4.

    The child rounds in a chain from the right: 2.348 becomes 2.35, and then 2.35 becomes 2.4. Only the digit right after the tenths place counts. That digit is 4, so the answer is 2.3.

    What helps. Have your child underline the rounding digit and circle the one digit to its right. Only the circled digit decides.

  • Your child rounds 6.97 to the nearest tenth and writes 6.10.

    The 9 goes up by one and becomes 10, and the child writes the whole 10 in the tenths place. Rounding a 9 up carries into the ones place, just as 69 + 1 = 70.

    What helps. Ask which two tenths 6.97 sits between. Count by tenths together: 6.8, 6.9, 7.0. The tenth after 6.9 is 7.0, so 6.97 rounds to 7.0.

  • Asked to round 53.27 to the nearest tenth, your child writes 50.

    "Tens" and "tenths" sound almost the same. The child rounds to the tens place, which is to the left of the decimal point. The answer should be 53.3.

    What helps. Point out that every place name ending in "th" is to the right of the decimal point. A quick place-value chart with the point in the middle makes the difference easy to see.

Try four practice questions

Real 5th grade questions from our question bank, easiest first. Answer them right here, check each one, and see a worked solution for any question.

  1. 1Warm-up
    The decimal below will be rounded to the nearest one.
    6.482\displaystyle 6.482
    Select the digit that decides whether the number rounds up or down.
    A
    4
    B
    6
    C
    8
    D
    2
    Show the answer and how to solve it

    The answer is 4 because 4 is immediately to the right of the ones digit in 6.482.

    1. 1To round to the nearest one, first find the ones digit. In 6.482, the ones digit is 6.
    2. 2The deciding digit is always the digit immediately to the right of the place you are rounding to. The digit to the right of the ones place is 4, in the tenths place.
    3. 3So 4 is the digit that tells whether the number rounds up or down.

    Common mistake. A common mistake is choosing 6 because it is the ones digit. The deciding digit is the next digit to the right, which is 4.

    The idea underneath. When rounding to any place, the only digit that decides the round-up or round-down choice is the digit immediately to its right.

  2. 2On level
    Round the decimal shown below to the nearest tenth.
    0.47\displaystyle 0.47
    Select the rounded number.
    A
    0.5\displaystyle 0.5
    B
    0.4\displaystyle 0.4
    C
    0.7\displaystyle 0.7
    D
    0.0\displaystyle 0.0
    Show the answer and how to solve it

    The answer is 0.5 because the 7 in the hundredths place tells you to round the 4 in the tenths place up to 5.

    1. 1Look at the decimal shown.
    2. 2The tenths digit is 4.
    3. 3Halfway between 0.40.4 and 0.50.5 is 0.450.45. Since 0.47>0.450.47 > 0.45, the nearer tenth is 0.50.5.

    Common mistake. A common mistake is choosing 0.4 and not checking the hundredths digit. In 0.47, the hundredths digit is 7, so the tenths digit must round up.

    The idea underneath. Rounding to the nearest tenth means choosing the closest tenth. Neighboring tenths are 10 hundredths apart, so 5 hundredths is halfway. At halfway, choose the greater tenth.

  3. 3On level
    Round the decimal shown below to the nearest thousandth.
    3.15267\displaystyle 3.15267
    Select the rounded number.
    A
    3.153\displaystyle 3.153
    B
    3.152\displaystyle 3.152
    C
    3.150\displaystyle 3.150
    D
    3.162\displaystyle 3.162
    Show the answer and how to solve it

    The answer is 3.153 because the 6 to the right of the thousandths digit tells you to round 2 up to 3.

    1. 1Find the thousandths digit. It is the third digit to the right of the decimal point.
    2. 2In 3.15267, the thousandths digit is 2. The next digit is 6, so you round up.
    3. 3Increase the 2 by 1 and keep 3 digits after the decimal point.
    4. 4So the correct choice is 3.153.

    Common mistake. A common mistake is choosing 3.152 because it stops at three decimal places without checking the next digit. When rounding to the nearest thousandth, always look at the digit right after the thousandths place.

    The idea underneath. To round to a place value, keep digits through that place and let the digit immediately to the right decide whether the last kept digit stays the same or increases by 1.

  4. 4Stretch
    Round the decimal below to the nearest hundredth.
    4.597\displaystyle 4.597
    Enter the rounded decimal.
    Show the answer and how to solve it

    Answer. 4.60

    The rounded decimal is 4.60 because the thousandths digit 7 forces the hundredths digit 9 to round up, carrying 1 into the tenths place and changing 5 to 6.

    1. 1Start at the hundredths place. It is the second digit to the right of the decimal point.
    2. 2In 4.597, the hundredths digit is 9 and the thousandths digit is 7.
    3. 34.595 is halfway between 4.59 and 4.60. 4.597 is above that halfway point, so it is closer to 4.60. The hundredths digit is 9, so 9+1=109 + 1 = 10: write 0 in the hundredths place and carry 1 to the tenths place. The tenths digit 5 becomes 6, giving 4.60.

    Common mistake. A common mistake is writing 4.59. That truncates the decimal instead of rounding, because a thousandths digit of 7 means the hundredths digit must increase.

    The idea underneath. Rounding to the nearest hundredth means choosing the closer hundredth. If a number is exactly halfway, round up.