Rounding, significant figures & estimation

To round to a given place value, look at the digit immediately to its right. If that digit is 5 or more, round up; if it is 4 or less, round down, leaving the rest as zeros. So 73 to the nearest 10 is 70 (the units digit 3 rounds down), 248 to the nearest 100 is 200 (the tens digit 4 rounds down), and 6480 to the nearest 1000 is 6000 (the hundreds digit 4 rounds down). The digit you are checking is the only one that matters — ignore everything further to the right.

Significant figures count from the first non-zero digit of a number, left to right. They are useful because they describe how precise a number is regardless of its size. To round 2473 to 1 significant figure, keep the leading 2 and look at the next digit (4) to round: 2473 → 2000. To round 38500 to 2 significant figures, keep 3 and 8, and the next digit 5 rounds up, giving 39000.

For small decimals the leading zeros are placeholders, not significant, so you start counting at the first non-zero digit. 0.0456 to 1 significant figure is 0.05 (start at the 4, the next digit 5 rounds up), and 0.04825 to 2 significant figures is 0.048. This is what makes significant figures different from decimal places: 0.0456 to 1 decimal place would be 0.0, but to 1 significant figure it is 0.05. Watch for a carry — rounding 9962 to 2 significant figures rolls 99 up to 100, giving 10000.

The fastest estimate rounds every number to 1 significant figure and then does the easy calculation. To estimate 6.2 × 48, round to 6 × 50 = 300; the real answer, 297.6, is close, so it is sensible. For 6120 ÷ 29, round to 6000 ÷ 30 = 200. Estimation will not give the exact answer, but it tells you the right ballpark, which is enough to catch a slipped decimal point or an extra zero.

Type the rounded number or estimate as a plain number — no units. You may include commas in large numbers if you like (40,000 and 40000 are both accepted). For decimal answers, type the decimal exactly, such as 0.05 or 0.048.