Estimating with decimals

To estimate with decimals, round each number to a whole number or a friendly number, then do the easy calculation in your head.

Why estimating matters with decimals

Most decimal mistakes are about the decimal point: an answer ten times too big or ten times too small. An estimate catches these at once. If 4.8 × 3.1 should be about 15, then an answer of 1.488 or 148.8 must be wrong.

Estimating is also how adults really use decimals. “Have I got enough money?” and “Will this shelf fit?” need only a rough answer. A rough answer in two seconds often beats an exact one in two minutes.

See it: pictures to draw with your child

Copy these onto paper or a whiteboard. A quick sketch makes the idea concrete before any written method.

6.7 is closer to 7 than to 6, so it rounds to 7.

3.2 is closer to 3, so it rounds down.

Round each price up: about $10 in total.

Round each number to the nearest whole number

The simplest estimate rounds every decimal to the nearest whole number. Look at the tenths digit: 5 or more rounds up, less than 5 rounds down. So 6.7 → 7 and 3.2 → 3.

For example, 6.7 + 3.2 ≈ 7 + 3 = 10, and the exact answer is 9.9. In the same way, 8.45 − 2.9 ≈ 8 − 3 = 5, and the exact answer is 5.55. See rounding decimals.

Use friendly numbers

Sometimes a friendlier number than the nearest whole gives an easier sum. For division, choose numbers that divide neatly: 17.8 ÷ 3.1 ≈ 18 ÷ 3 = 6. For money, round to the nearest dollar or to half dollars: $4.49 + $2.55 ≈ $4.50 + $2.50 = $7.

Compatible numbers like these are allowed to be a little further away, as long as the calculation becomes easy to do in your head.

Estimating products and quotients

For multiplication, round each factor: 4.8 × 3.1 ≈ 5 × 3 = 15, and the exact answer is 14.88. For decimals less than 1, think of fractions: 0.48 × 60 is about half of 60, which is 30.

For division, ask “about how many times?”: 9.6 ÷ 2.4 is about 10 ÷ 2.5 = 4, and the exact answer is 4. See dividing decimals.

Estimating at the shops

Rounding prices up gives a safe estimate. If every item is rounded up, you know you have enough money.

For example, $2.35, $4.80 and $1.15 round up to $3, $5 and $2, so $10 is plenty. The exact total is $8.30. See decimals and money.

Is the estimate over or under?

Good estimators know which way they rounded. If both numbers were rounded up, the estimate is too big.

If both were rounded down, it is too small. Asking “will the real answer be more or less than my estimate?” builds real number sense.

Tips for teaching estimating

Ask for an estimate before every decimal calculation, not just in estimating lessons. Write it in a box next to the working. After the exact answer, children circle whether it was close.

Praise good reasoning, not just closeness. “I rounded both up, so the real answer is a bit less” is a better answer than a lucky guess.

Quick-fire rounds work well as warm-ups. Show a sum like 5.9 × 3.1 for five seconds and ask for an estimate. Children soon learn to round without writing anything down.

Quiz: estimating with decimals

Choose the best estimate, or round to the nearest whole number.

Where this fits: decimals step by step

What to say to your child

A short script for teaching it the first time. Pause after each line and let your child do the next step.

“A drink costs $1.95 and a sandwich $3.10. About how much?”
“Round them: $2 and $3.” (About $5.)
“Is the real answer more or less than $5?” (A tiny bit more: $5.05.)
“What is 4.8 × 3.1 roughly?” (5 × 3 = 15.)
“Someone says 148.8. Is that right?” (No, far too big.)

More worked examples

Example 1: addition

7.85 + 2.3 ≈ 8 + 2 = 10; exact 10.15.

Example 2: subtraction

9.1 − 4.75 ≈ 9 − 5 = 4; exact 4.35.

Example 3: multiplication

6.2 × 4.9 ≈ 6 × 5 = 30; exact 30.38.

Example 4: division

15.6 ÷ 3.9 ≈ 16 ÷ 4 = 4; exact 4.

Practice questions (answers below)

Ask these out loud or write them down. Check each answer, and ask “how did you get that?” for one or two.

Round 4.6 to the nearest whole number
Round 12.38 to the nearest whole number
Estimate 3.8 + 5.1
Estimate 9.7 − 2.2
Estimate 5.9 × 4
Estimate 19.8 ÷ 4.1
Estimate $2.95 + $6.10
Is 3.9 × 2.1 = 81.9 sensible?
Estimate 0.52 × 80
Stretch: estimate 48.7 ÷ 0.98

Show the answers

5
12
About 9
About 8
About 24
About 5
About $9
No: about 8, so 8.19
About 40
About 50

Common mistakes

Rounding the wrong digitRounds 6.47 to 7 because of the 7.Fix: look only at the tenths digit: 4, so 6.

Estimating, then not using itGets 148.8 for 4.8 × 3.1 and moves on.Fix: compare the answer with the estimate of 15.

Rounding too farRounds 0.48 to 0 and gets 0 × 60 = 0.Fix: use friendly numbers: 0.48 is about one half.

How to teach it at home

Trolley total

Estimate the shopping total before the till does.

Fuel guess

Estimate the cost of fuel from the price per litre.

Over or under

After each estimate, ask whether the real answer is more or less.

By grade

Grade 5 (5.NBT.A.4, 5.NBT.B.7): round decimals and estimate to check calculations.
Grade 6 (6.NS.B.3): estimate before multi-digit decimal calculations.
Next: decimals and money.

More for each grade: Grade 5 math and the CBSE class 5 maths guide; Grade 6 math and the CBSE class 6 maths guide.