98.32 correct to the nearest whole number is □.

98. Look at the first decimal place, 3: 5 or more rounds up, otherwise it drops. So 98.

63.274 rounded down to 1 decimal place is □.

63.2. Rounding down: everything after the first decimal place goes, however big. So 63.2.

A bag of beans weighs 200 g. 10 g holds about 44 beans. About how many beans are in the bag?

880 beans. 200 g is 20 times 10 g: 20 × 44 = 880 beans.

Numbers and operations · Ages 12–13

Approximation & estimation

From “Rounding off to a place value” to “Planning an estimate”, step by step, each skill with its methods, worked examples and answers.

Skills and methods in this topic, easy to hard

Rounding off to a place valueLook at the one digit after the place you keep: 5 or more rounds up
Method3,462 to the nearest hundred: 6 follows, so 3,500
Another way: Halfway on a number lineHalfway between 3,400 and 3,500 is 3,450; 3,462 is nearer 3,500
Rounding to decimal placesLook at the next decimal place; write every decimal place asked for
Method2.4371 ≈ 2.44 (to 2 d.p.)
Another way: Count in hundredths2.4371 = 243.71 hundredths ≈ 244 hundredths = 2.44
Significant figuresCount from the first digit that isn't 0; fill whole numbers with zeros
Method0.004070 has 4 s.f.; 34,567 ≈ 35,000 (2 s.f.)
Another way: As digits times a power of 100.004070 = 4.070 × 0.001: 4 figures
Rounding up and rounding downUp: anything left, go up one; down: drop the rest
Method3.41: up 3.5, down 3.4, off 3.4 (1 d.p.)
Another way: The mark right or left3.41 is between 3.4 and 3.5: up takes 3.5, down 3.4
Estimation strategies1 s.f., front-end or compatible numbers; then over or under
Method382 × 47 ≈ 400 × 50 = 20,000 (an overestimate)
Another way: Compatible numbers4,213 ÷ 7 ≈ 4,200 ÷ 7 = 600
Estimating when shoppingEnough money? Round up. Reached a total? Round down
Method13 + 24 + 10 = 47 ≤ 50, so $50 is surely enough
Another way: Work it out exactly12.8 + 23.5 + 9.9 = 46.2 ≤ 50
Planning an estimateBig side or small side, which method, how precise
Method20 squares × about 35 people ≈ 700 people
Another way: Estimate with a rate3 drops every 10 s: 86,400 ÷ 10 × 3 = 25,920 drops

Worked examples

From different skills in this topic. Have a go first, then open each one for the answer and the working.

Example 1Rounding off to a place value →
98.32 correct to the nearest whole number is .
Show the answer and working
Answer: 98
Look at the first decimal place, 3: 5 or more rounds up, otherwise it drops. So 98.
Example 2Rounding up and rounding down →
63.274 rounded down to 1 decimal place is .
Show the answer and working
Answer: 63.2
Rounding down: everything after the first decimal place goes, however big. So 63.2.
Example 3Planning an estimate →
A bag of beans weighs 200 g. 10 g holds about 44 beans. About how many beans are in the bag?
Show the answer and working
Answer: 880 beans
200 g is 20 times 10 g: 20 × 44 = 880 beans.

Free worksheet: Approximation & estimationWorking out, multiple choice and word problems, with answers and working, to print or save as a PDF

VIP practice notes and papers

Aimed at tests and exams: questions on this topic, new every time, to print or save as a PDF.

Practice notes: The key point, worked examples step by step, then questions of the same kind to follow, hints fading
Practice paper: Set out in parts like a school paper, marked, with answers and full working

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