Decimals · Grades 5

Rounding Decimals to Any Place

Quick answer

To round a decimal, find the place you are rounding to and look at the single digit immediately after it. If that digit is 5 or more, round up; if it is 4 or less, leave the place as it is. Either way, every digit after the rounding place is dropped. Rounding 3.47 to one decimal place gives 3.5, because the 7 pushes the 4 up.

What you'll learn

  • Round a decimal to a named place
  • Explain why only the next digit matters
  • Handle rounding that carries into the place before

The rule

  1. Find the place you are rounding to.
  2. Look at the one digit immediately after it.
  3. That digit is 55 or more — round the place up. It is 44 or less — leave the place alone.
  4. Drop everything after the rounding place.

Round 3.473.47 to one decimal place. The tenths place holds 44; the next digit is 77.

3.47⟶3.53.47 \quad\longrightarrow\quad 3.5

Why rounding is really “which is it nearer to”

The rule is a shortcut for a question about distance. 3.473.47 sits between 3.43.4 and 3.53.5 — which is it closer to?

3.47 is nearer to 3.5 than to 3.4 A number line from 3.4 to 3.5 divided into hundredths, with a dot at 3.47 sitting past the midpoint at 3.45, closer to 3.5. 3.4 3.41 3.42 3.43 3.44 3.45 3.46 3.47 3.48 3.49 3.5 halfway 3.47
3.47 is nearer to 3.5 than to 3.4

The midpoint is 3.453.45. Anything past it is nearer to 3.53.5, and 3.473.47 is past it, so it rounds up.

That is all the “5 or more” rule is doing: the next digit tells you which side of the midpoint you landed on, because the midpoint always has a 55 in that place.

Why only one digit matters

A common worry: does 3.44993.4499 round up, since those nines are almost enough?

No. The hundredths digit is 44, so the number is below 3.453.45 — below the midpoint. Nines further right can creep towards 3.453.45 but never reach it, so the answer is 3.43.4.

The digit immediately after the rounding place has already settled which side of halfway you are on. Everything beyond it is too small to change that.

When rounding up carries

If the digit being rounded up is a 99, it becomes 1010 of that place — which is one of the place before, exactly as in addition.

2.97⟶3.02.97 \quad\longrightarrow\quad 3.0

Nine tenths plus one more tenth is ten tenths, which is one whole. The 22 becomes 33 and the tenths place resets to 00.

Keep that zero. "3.03.0" says the answer is correct to one decimal place; "33" claims only whole-number precision.

Rounding once, at the end

Each rounding introduces a small error, and later steps carry it forward. Rounding 8%8\% of $72 to $6 before adding gives a total of $78 instead of $77.76.

So carry the full figure through the working and round only the final answer.

Worked examples

Common mistakes

Practice problems

  1. Round 4.624.62 to one decimal place.

    Answer

    4.64.6

    Full solution

    The digit after the tenths is 22, which is 44 or less, so the tenths place is unchanged.

  2. Round 4.674.67 to one decimal place.

    Answer

    4.74.7

    Full solution

    The digit after the tenths is 77, so the 66 rounds up to 77.

  3. Round 9.3489.348 to two decimal places.

    Answer

    9.359.35

    Full solution

    The digit after the hundredths is 88, so the 44 rounds up.

  4. Round 15.515.5 to the nearest whole number.

    Answer

    1616

    Full solution

    The digit after the ones place is exactly 55, and 55 or more rounds up.

  5. Round 7.967.96 to one decimal place.

    Hint

    The tenths digit is a 99.

    Answer

    8.08.0

    Full solution

    Rounding the 99 tenths up gives 1010 tenths, which is one whole. The 77 becomes 88 and the tenths reset to 00.

  6. Round 0.04720.0472 to two decimal places.

    Answer

    0.050.05

    Full solution

    The hundredths place holds 44 and the next digit is 77, so it rounds up to 55.

  7. Round 2.34992.3499 to one decimal place.

    Hint

    Only one digit is consulted.

    Answer

    2.32.3

    Full solution

    The digit after the tenths is 44, so the tenths place stays. The 9999 that follows is never looked at.

  8. A price of $12.994 is charged to the nearest cent. What is paid?

    Answer

    $12.99

    Full solution

    Cents are hundredths. The digit after them is 44, so the hundredths place is unchanged.

  9. Round 199.97199.97 to one decimal place.

    Hint

    The carry may travel more than one place.

    Answer

    200.0200.0

    Full solution

    The digit after the tenths is 77, so the 99 tenths round up to 1010 tenths — one whole.

    That whole carries into the 199199, which becomes 200200, and the tenths reset to 00.

  10. Sam rounds 3.4463.446 to hundredths first, getting 3.453.45, then rounds that to tenths and reports 3.53.5. Is that right?

    Hint

    Round the original number straight to tenths and compare.

    Answer

    No. The answer is 3.43.4.

    Full solution

    Rounding straight to tenths: the digit after the tenths is 44, so the tenths place stays and the answer is 3.43.4.

    Sam’s two-step route rounded up twice on a number that was never past halfway. 3.4463.446 is below 3.453.45, so it belongs to 3.43.4.

    Rounding in stages nudges a number upward at each step, which is exactly why you round once, to the place asked for.

Frequently asked questions

How do I round a decimal?

Find the place you are rounding to, then look at the one digit immediately after it. Five or more rounds up; four or less leaves it alone. Everything after the rounding place is then dropped.

Why do I only look at one digit?

Because that digit already decides which side of halfway you are on. In 3.4499 the 4 in the hundredths means the number is below 3.45, so it cannot reach halfway however many nines follow.

What happens if the digit is a 9 and it rounds up?

It carries, exactly as in addition. Rounding 2.97 to one decimal place makes the 9 become 10 tenths, which is one whole, so the answer is 3.0.

Do I keep the zero in 3.0?

Yes, when the question asked for one decimal place. The zero shows the precision you rounded to, so 3.0 says something 3 does not.

Why does rounding partway through a calculation cause errors?

Because each rounding adds a small error and later steps multiply it. Carry the full figure and round once, at the end.

What to learn next

Key terms in this lesson

Place value
Place value is the idea that a digit's worth depends on where it sits. The 4 in 40 is worth forty; the 4 in 0.4 is worth four tenths.

Standards alignment

This lesson covers the following Common Core State Standards for Mathematics.

For teachersTick to print a blank worksheet; leave it clear to print the lesson with the full answer key.