How to Round Numbers

1. Underline the digit in the place you're rounding to.
2. Look at the next digit to its right. Only this digit decides.
3. 5 or more: add 1 to the underlined digit. 4 or less: leave it.
4. Clean up: drop the digits after it, or turn them into zeros if they're before the decimal point.

Think of it as asking which of two neighbors the number is closer to. 2,847 sits between 2,800 and 2,900; it's below the halfway mark of 2,850, so it rounds to 2,800.

Take 6,382:

• Nearest ten: 6,382. The next digit is 2, so keep the 8: 6,380.
• Nearest hundred: 6,382. The next digit is 8, so the 3 becomes 4: 6,400.
• Nearest thousand: 6,382. The next digit is 3, so keep the 6: 6,000.

The digits after your place become zeros. They hold the place value, so 6,400 still means six thousand four hundred.

"Two decimal places" means the hundredths place. For 14.276:

• 1 decimal place: 14.276. The next digit is 7, so 14.3.
• 2 decimal places: 14.276. The next digit is 6, so 14.28.
• Whole number: 14.276. The next digit is 2, so 14.

After the decimal point, the extra digits are simply dropped, not turned into zeros. Money is usually rounded to 2 decimal places: $2.061675 becomes $2.06.

A 9 can't become 10 in one place, so it becomes 0 and carries 1 to the left, just like in addition:

• 2.97 to 1 decimal place → 3.0 (keep the 0 to show the precision)
• 9,960 to the nearest hundred → 10,000
• 3.996 to 2 decimal places → 4.00

Writing 3 instead of 3.0 isn't wrong in value, but 3.0 tells the reader the number was rounded to tenths.

Significant figures count meaningful digits from the first non-zero digit, wherever it is. That makes them handy in science, where numbers range from tiny to huge.

• 0.004567 to 2 s.f.: skip the leading zeros, keep 4 and 5, and the next digit 6 rounds up → 0.0046.
• 299,792,458 to 3 s.f.: keep 2, 9, 9; the next digit 7 rounds up and the 9s carry → 300,000,000.
• 48,519 to 2 s.f.: keep 4 and 8; the next digit 5 rounds up → 49,000.

Zeros: leading zeros never count, zeros between digits always count (405 has 3), and trailing zeros after a decimal point count (4.50 has 3).

"5 rounds up" is the school rule, but it's not the only one:

• Banker's rounding (half to even): an exact half goes to the even neighbor, so 2.5 → 2 but 3.5 → 4. Over many numbers the ups and downs cancel out, which is why it's used in accounting and many programming languages.
• Always up (ceiling): 2.1 → 3. Use it when you need enough of something: 23 people in cars of 5 need 5 cars, not 4.6.
• Always down (floor) or truncate: 2.9 → 2. Use it when only whole items count: $10 buys 3 notebooks at $3, not 3.33.

For negative numbers, "half up" usually means away from zero: −2.5 → −3.

Round each number to one or two significant figures, do the easy sum, and you have a check on any calculator answer:

If the calculator shows 7,990 or 10.29, you know a key was missed. Estimates use rounded numbers on purpose; the final answer should not.

• Rounding in stages: 3.447 → 3.45 → 3.5 is wrong. Round the original once: 3.447 to 1 decimal place is 3.4.
• Looking at the wrong digit: only the digit right after your place decides, not the last digit of the number.
• Dropping digits before the point: 6,382 to the nearest hundred is 6,400, not 64.
• Rounding too early: keep full precision until the final step, or small errors add up.

Check your answers with the Rounding Calculator.

1. 6,382 to the nearest ten
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   6,380
2. 6,382 to the nearest hundred
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   6,400
3. 14.276 to 1 decimal place
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   14.3
4. 0.0849 to 2 decimal places
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   0.08. The deciding digit is 4.
5. 3.996 to 2 decimal places
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   4.00. The 9s carry all the way to the ones place.
6. 48,519 to 2 significant figures
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   49,000
7. 0.07063 to 3 significant figures
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   0.0706. The zero between 7 and 6 counts.
8. 6.5 to a whole number with banker's rounding
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   6. An exact half goes to the even neighbor.