Year 10 Foundation · Rounding and estimation
Round to a given number of decimal places
Learn how to put numbers and decimals in order of size and round any number to a given number of decimal places.
Definition
Decimals extend place value beyond the ones column: the first digit after the point is tenths, the next is hundredths, then thousandths. Because every column is worth ten times the column to its right, the size of a decimal is decided place by place from the left, not by how many digits it has. Ordering decimals and rounding them both come down to reading these place values correctly.
Why Do I Have to Learn This?
Decimals are how we write amounts between whole numbers, like money and measurements. Prices, heights and race times all use them.
Key Rules:
- 1. To round to a given number of decimal places, keep exactly that many digits after the point and look only at the single digit that comes next.
- 2. If that next digit is 5 or more, round the last kept digit up; if it is 4 or less, leave the kept digits alone.
- 3. Keep any final zero the rounding produces: 12.396 to 2 decimal places is 12.40, not 12.4.
Remember:
- •Compare decimals place by place from the left, and let one digit decide a rounding: 5 or more rounds up.
Don’t Forget...
- •Rounding in stages: turning 3.649 into 3.65 and then into 3.7 when rounding to 1 decimal place. Only the single digit after the cut decides, and here it is 4, so 3.649 rounds to 3.6. It sits closer to 3.6 than to 3.7, and rounding twice loses that.
- •Dropping the final zero and writing 12.4 as the answer to 2 decimal places. An answer to 2 decimal places must show two digits after the point, so the zero in 12.40 is part of the answer, not an extra.
Decimal
A number written with a decimal point.
0.5 is the same as a half.
Worked Example:
Round 12.396 to 2 decimal places.
Keep two digits after the point, so the cut falls after 12.39.
Look at the next digit only: it is 6, which is 5 or more, so round up.
Rounding 12.39 up moves the 9 to 10 and carries: 12.39 becomes 12.40.
Write the final zero, because the question asks for two decimal places.
Answer: 12.40
Why It Works:
Each place value column is worth ten times the column to its right, so a bigger digit further left outweighs every digit that follows it, and comparing from the left must give the right order. Rounding works because the digit after the cut tells you which of the two possible answers is nearer: a 5 or more means the number is at least halfway to the one above.
Another Example:
Write these numbers in order from smallest to largest: 0.72, 0.7, 0.68, 0.702
Give every number three decimal places by writing zeros on the end: 0.720, 0.700, 0.680, 0.702.
Compare the tenths first: 0.680 has 6 tenths and the rest have 7, so 0.68 is the smallest.
Compare the hundredths of the rest: 0.700 and 0.702 have 0 hundredths, while 0.720 has 2, so 0.72 is the largest.
Split 0.700 and 0.702 using the thousandths: 0 is less than 2, so 0.7 comes before 0.702.
Answer: 0.68, 0.7, 0.702, 0.72
Animated Example:
Free Round to a given number of decimal places Worksheet
Download free worksheets and practise today.
Every download has a fresh set of questions.
Before this: Place value, ordering and rounding (Year 7)
Let’s Practise the Concept
Step 1 of 3
Put the decimals in order
Tap them from smallest to largest.
In order so far: nothing yet