Rounding to decimal places and significant figures
Round numbers and measures to an appropriate degree of accuracy, including a specified number of decimal places or significant figures.
What a learner can do afterwards
- Round numbers to a given number of decimal places
- Round numbers to a given number of significant figures
- Choose an appropriate degree of accuracy for a given context
1 · Read
Decimal places count every digit after the point, including zeros. One place ends at tenths, two at hundredths and three at thousandths. Use the rounding rule you know: check the digit just after the last place to keep. Here, 5 or more means increase that place by 1; below 5 means leave it unchanged. Remove later decimal digits. Keep zeros needed to show the requested places, as in 3.40.
Round 12.3746 km to 2 decimal places. Keep the tenths and hundredths digits, 3 and 7. Check the next digit, 4. A next digit below 5 leaves the kept place unchanged; 5 or more would increase it by 1. Here the 7 stays unchanged, so the answer is 12.37 km.
Significant figures start at the first nonzero digit. Ignore earlier zeros. Zeros between significant digits and ending zeros after the decimal point count. In 0.00620, the significant figures are 6, 2 and 0. To round to a chosen number of significant figures, find the last digit to keep. Check the next digit: 5 or more increases the kept place by 1; below 5 leaves it unchanged.
Round 12.3746 km to 3 significant figures. Keep 1, 2 and 3. The next digit is 7, so the 3 becomes 4: 12.4 km. For a small decimal, skip leading zeros. To round 0.0246 to 2 significant figures, keep 2 and 4. The next digit is 6, so the result is 0.025. Keep the leading zeros to preserve the number's size.
Choose accuracy from the task. Nearest centimetre means 2 decimal places in metres, because 0.01 m is 1 cm. For a rough estimate, fewer digits may be enough. To compare close measurements, keep enough detail to tell them apart. Writing extra digits or adding zeros cannot improve the measuring tool or recover detail it did not record.
Rounding can carry through several 9s. To round 2.998 to 2 decimal places, check 8. Add 0.01 to 2.99 to get 3.00. Keep both zeros to show 2 decimal places. For significant figures, count the rounded result again after a carry: 0.0997 to 2 significant figures becomes 0.10, with 1 and the ending 0 significant.
When significant-figure rounding ends before the ones place, replace later whole-number digits with zeros to keep place value. For 4,861 to 2 significant figures, keep 4 and 8, check 6 and round to 4,900. Its ending zeros hold place value. A measurement written as 4,900 does not by itself tell us which ending zeros were measured. Keep the instruction 'to 2 significant figures' beside the rounded value.
Different numbers can round to the same value. For example, 4.62 and 4.64 both round to 4.6 to 1 decimal place: the next digits, 2 and 4, are below 5. The rounded value has lost some detail. It cannot tell you which original number was larger.
When asked to round a sum, add first. Line up decimal points and add each column from right to left, carrying when needed. For example, 2.136 + 1.136 = 3.272, which rounds to 3.27 to 2 decimal places. Rounding separately gives 2.14 + 1.14 = 3.28, a different result. Use the full numbers until the final sum.
Round directly to the requested accuracy. Rounding twice can change the result: 4.349 to 2 decimal places is 4.35, which then rounds to 4.4 to 1 decimal place. Directly rounding 4.349 to 1 decimal place checks the 4 in the hundredths place and gives 4.3. Check the digit immediately after the final kept place in the original number.
For a missing digit, test which digits fit the rounding rule. If 3.2? rounds to 3.3 to 1 decimal place, ? can be 5 through 9. If 3.?6 rounds to 3.5 to 1 decimal place, the 6 increases the kept digit by 1, so ? must be 4. Use the same check when significant figures choose the kept place.
Look at the digit right after your cut-off point: 5 or more rounds the last digit up, below 5 leaves it the same.
The lesson, quiz questions and flashcards were written for this dataset.
Questions x1 to x4 and x6 to x12, and all four readings, were written for this dataset. Question x5 adapts the two-decimal rounding task in Robert Kaplinsky's Rounding Decimals 2 at Open Middle. The two linked videos are from Khan Academy.
More to read
Choosing how much detail to keep
Find out what a measurement record is for before rounding it. A form might ask for metres to the nearest centimetre. That means keeping two decimal places, because 0.01 m is 1 cm.
Close measurements may need more detail. Race times of 14.32 s and 14.34 s both become 14.3 s when rounded to tenths. Those entries hide the difference between the runners.
Writing extra digits does not improve the measuring tool. Use the detail supported by the measurement and needed for the task. Rounding changes how you report a value; it cannot repair a measuring mistake.
Which zeros count?
Decimal places count all digits after the decimal point. The value 6.00 has two decimal places. Its ending zeros show how the value was recorded.
For significant figures, begin at the first nonzero digit. In 0.00540, skip the zeros before 5, then count 5, 4 and the ending 0. That is three significant figures. Zeros between significant digits count too: 2.003 has four significant figures.
Whole-number ending zeros need context. A measurement written as 4,700 does not tell you whether its ending zeros were measured or only hold place value. If rounding to two significant figures gives 4,700, keep that rounding instruction beside the value.
Carries and direct rounding
A rounding increase can move through several columns. For 9.996 to two decimal places, keep 9.99 and check 6. Add one hundredth: 9.99 + 0.01 = 10.00. Both ending zeros are needed to show two decimal places.
Use the original value to choose the decision digit. For example, 6.349 rounds directly to 6.3 to one decimal place, because its hundredths digit is 4.
Another route can give a different result. First rounding 6.349 to two decimal places gives 6.35. Rounding that value to one decimal place gives 6.4. Round directly to the requested accuracy to avoid this change.
Two ways to shorten a number
Decimal places and significant figures can select different kept digits in the same number.
Take 0.02746. For two decimal places, count two places after the point. Keep 0.02 and check 7. The result is 0.03.
For two significant figures, skip the leading zeros and keep 2 and 7. The next digit is 4, so the result is 0.027.
Both answers follow a rounding instruction, but the instructions differ. Read which method and how many digits the task requests. Then check the digit immediately after the last one you will keep.
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