Number
Grade 2-3Rounding & Significant Figures
Rounding questions look simple but hide two separate skills, decimal places and significant figures follow different rules for finding the digit that matters. This lesson covers rounding to a given number of decimal places, rounding to significant figures, and rounding whole numbers to a given place value.
Written by Asad, Co-Founder of Teachably
Video walkthrough coming soon
The written lesson below covers everything you need in the meantime.
Rounding to a whole-number place value
To round to the nearest 10, 100 or 1000, find the digit in that place value column, then look at the digit immediately to its right. If that digit is 5 or more, round up; if it is less than 5, round down. Every digit to the right of the rounded place becomes a zero.
3847 to the nearest 100: the hundreds digit is 8, and the digit to its right is 4, which is less than 5, so round down to 3800.
Rounding to a number of decimal places
Count along from the decimal point to the place you are rounding to, then look at the next digit after it. If that digit is 5 or more, round the previous digit up; if it is less than 5, leave it as it is. Every digit after the rounded place is removed.
5.738 to 1 decimal place: the first decimal digit is 7, and the next digit is 3, which is less than 5, so the answer is 5.7.
Rounding to significant figures
The first significant figure is the first non-zero digit, reading from the left. Leading zeros in a decimal like 0.0524 are not significant, so the significant figures start at the 5. Count the required number of significant figures from there, then round using the next digit exactly as with decimal places.
4273 to 2 significant figures: the first two significant figures are 4 and 2, and the next digit is 7, which is 5 or more, so round up to 4300. 0.05237 to 3 significant figures: the significant figures are 5, 2, 3, and the next digit is 7, so round up to 0.0524.
Rounding money to the nearest penny
Money is rounded the same way as decimal places, since the nearest penny is 2 decimal places. Look at the third decimal digit to decide whether the second decimal digit rounds up or stays the same.
£24.376 to the nearest penny: the second decimal digit is 7, and the next digit is 6, which is 5 or more, so round up to £24.38.
Worked Examples
Three exam-style questions, fully solved.
Round 3847 to the nearest 100.
Easy- 1.Find the hundreds digit: 8
- 2.Look at the digit to its right, the tens digit: 4, which is less than 5, so round down
Answer: 3800
Round 4273 to 2 significant figures.
Medium- 1.The first two significant figures are 4 and 2
- 2.Look at the next digit, 7, which is 5 or more, so round up
- 3.Round the second significant figure up from 2 to 3, and replace the remaining digits with zeros
Answer: 4300
Round 0.05237 to 3 significant figures.
Hard- 1.Leading zeros are not significant, so the significant figures start at the 5: 5, 2, 3
- 2.Look at the next digit, 7, which is 5 or more, so round up
- 3.Round the third significant figure up from 3 to 4, keeping the leading zeros
Answer: 0.0524
Avoid These
The most common mistakes students make.
Rounding a whole number to the nearest 100 or 1000 but forgetting to replace the remaining digits with zeros, for example writing 38 instead of 3800.
Treating significant figures the same as decimal places, and not realising that leading zeros in a number like 0.0524 do not count as significant figures.
Looking at the wrong digit to decide whether to round up, for example checking two places along instead of the single digit immediately after the one being rounded.
Rounding a number in stages, for example rounding 4.449 to 1 decimal place first and getting 4.5, then rounding that to a whole number and getting 5, instead of rounding directly from the original figure.
Dropping the trailing zero when rounding money to the nearest penny, for example writing £24.4 instead of £24.40 when the second decimal digit is a zero.
FAQ
Questions parents and students ask.
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