---
title: "Estimation Practice Questions: Is Your Estimate Too Big or Too Small?"
url: https://www.learningloftinstitute.com/practice/estimation-and-checking-practice-questions
source: Learning Loft Institute
language: en
updated: 2026-08-21
section: "Practice › Estimation Practice Questions: Is Your Estimate Too Big or Too Small?"
---
# Estimation Practice Questions: Is Your Estimate Too Big or Too Small?
> **Answer.** Estimating means rounding each number to one significant figure and doing that easier calculation. For 38 × 21, round to 40 × 20 = 800. The exact value is 798, so the estimate is 2 too high. Rounding a factor up, or a divisor down, always pushes an estimate above the true answer.
## One significant figure is not one decimal place
The first significant figure of a number is its first non-zero digit, wherever that digit happens to sit. In 812 it is the 8, so 812 becomes 800. In 0.052 it is the 5, so 0.052 becomes 0.05 — not 0.1, and not 0.0. Small decimals are where this goes wrong most often, and when it does the rounded number is out by a factor of ten before any arithmetic has started.
The test of whether you have rounded correctly is whether the calculation is now doable in your head. 600 ÷ 30 is a mental step. 612 ÷ 29 is not. If the rounded version still needs a calculator, you have not rounded far enough.
## You can say whether the estimate is high or low before you check
Every rounding either raises a number or lowers it, and each of those moves the answer in a direction you can name in advance. That is what separates an estimate from a guess — it comes with a known lean.
Two of them cover division, and they are the ones pupils get backwards. A larger divisor makes an answer smaller, so rounding 29 up to 30 pushes 612 ÷ 29 down. Say that sentence once and the rule stops needing to be memorised.
- Round a number you are multiplying up, and the estimate goes up.
- Round a number you are multiplying down, and the estimate goes down.
- Round the number being divided up, and the estimate goes up.
- Round the divisor up, and the estimate goes down. Round the divisor down, and the estimate goes up.
## When the two roundings pull opposite ways
If both roundings push the same way the answer is certain. 19.6 ÷ 0.42 became 20 ÷ 0.4 — numerator up, divisor down — so 50 has to be too big, and it is: the true value is 46.67 to two decimal places.
When they disagree you have to compare their sizes, and that comparison is quick. In 38 × 21 → 40 × 20, raising 38 to 40 adds 2 × 21 = 42, while dropping 21 to 20 removes 40 × 1 = 40. The gain wins by 2, which is exactly the error in the estimate.
This is also the honest answer to "why not just use the calculator". The estimate is what tells you the calculator answer is plausible. Working out the exact value first and then rounding it answers a different question, and it shows: an "estimate" of 798 for 38 × 21 gives away that the full multiplication was done.
## Common mistakes
- Rounding 0.052 to 0.1 or to 0.0 by counting decimal places instead of significant figures, which puts the estimate out by a factor of ten.
- Predicting an over-estimate whenever numbers are rounded up, forgetting that rounding a divisor up makes the answer smaller.
- Working out the exact answer on a calculator and then rounding it, which answers a different question and shows in the working.
- Rounding to two significant figures because it feels more accurate, leaving a calculation like 610 ÷ 29 that still cannot be done mentally.
- Rounding 4.8 × 7.2 to 5 × 7 correctly but then writing 35 as the exact answer as well.
## Practice questions
### Question 1
Estimate 38 × 21 by rounding each number to 1 significant figure. Then work out the exact value and say whether the estimate is too big or too small.
**Answer:** Estimate 800; exact 798; a slight over-estimate
1. 38 rounds to 40 and 21 rounds to 20.
2. 40 × 20 = 800.
3. Exact: 38 × 21 = 798.
4. Raising 38 to 40 adds 2 × 21 = 42; lowering 21 to 20 removes 40 × 1 = 40.
5. Net effect +2, so the estimate is 2 above the true value.
### Question 2
Estimate 612 ÷ 29 by rounding to 1 significant figure, and state whether your estimate is above or below the exact answer.
**Answer:** Estimate 20; exact 21.1 (1 d.p.); an under-estimate
1. 612 rounds to 600 and 29 rounds to 30.
2. 600 ÷ 30 = 20.
3. Exact: 612 ÷ 29 = 21.103…
4. The number being divided was rounded down and the divisor was rounded up.
5. Both changes make a quotient smaller, so 20 must be below the true value.
### Question 3
Estimate 4.8 × 7.2 to 1 significant figure, then find the exact product and the size of the error.
**Answer:** Estimate 35; exact 34.56; over-estimate by 0.44
1. 4.8 rounds to 5 and 7.2 rounds to 7.
2. 5 × 7 = 35.
3. Exact: 4.8 × 7.2 = 34.56.
4. Raising 4.8 to 5 adds 0.2 × 7.2 = 1.44; lowering 7.2 to 7 removes 5 × 0.2 = 1.00.
5. 1.44 − 1.00 = 0.44, and 34.56 + 0.44 = 35.
### Question 4
Estimate 9.7 + 12.4 + 5.6 by rounding each number to 1 significant figure. Is the estimate high or low?
**Answer:** Estimate 26; exact 27.7; an under-estimate by 1.7
1. 9.7 → 10, 12.4 → 10, 5.6 → 6.
2. 10 + 10 + 6 = 26.
3. Exact: 9.7 + 12.4 + 5.6 = 27.7.
4. 12.4 lost 2.4 in the rounding, while 9.7 and 5.6 gained only 0.3 and 0.4.
5. −2.4 + 0.3 + 0.4 = −1.7, so the estimate is 1.7 low.
### Question 5
Estimate (58 × 31) ÷ 19.
**Answer:** Estimate 90; exact 94.6 (1 d.p.); an under-estimate
1. 58 → 60, 31 → 30, 19 → 20.
2. (60 × 30) ÷ 20 = 1800 ÷ 20 = 90.
3. Exact: 58 × 31 = 1798, and 1798 ÷ 19 = 94.63…
4. Rounding the divisor 19 up to 20 on its own drops the value to 1798 ÷ 20 = 89.9.
5. Raising 58 to 60 does not recover that loss, so 90 sits below the true value.
### Question 6
Estimate 0.38 × 812 and state the error.
**Answer:** Estimate 320; exact 308.56; over-estimate by 11.44
1. The first significant figure of 0.38 is the 3, so 0.38 rounds to 0.4.
2. 812 rounds to 800.
3. 0.4 × 800 = 320.
4. Exact: 0.38 × 812 = 308.56.
5. Raising 0.38 by 0.02 adds 0.02 × 812 = 16.24; dropping 12 from 812 removes 0.4 × 12 = 4.80. Net +11.44.
### Question 7
A theatre sells 412 tickets at PKR 1,850 each. Estimate the takings, then say whether the estimate is above or below the true figure.
**Answer:** Estimate PKR 800,000; exact PKR 762,200; an over-estimate
1. 412 rounds to 400 and 1,850 rounds to 2,000.
2. 400 × 2,000 = 800,000.
3. Exact: 412 × 1,850 = 762,200.
4. The price was rounded up by PKR 150 on every one of the 412 tickets, adding PKR 61,800.
5. Dropping 12 tickets removes only PKR 24,000, so the estimate finishes PKR 37,800 too high.
### Question 8
Estimate 19.6 ÷ 0.42.
**Answer:** Estimate 50; exact 46.67 (2 d.p.); an over-estimate
1. 19.6 rounds to 20 and 0.42 rounds to 0.4.
2. 20 ÷ 0.4 = 50, because 0.4 fits into 20 fifty times.
3. Exact: 19.6 ÷ 0.42 = 46.666…
4. The number being divided went up and the divisor went down.
5. Both push a quotient upwards, so 50 is above the true value.
### Question 9
A car covers 187 miles on 4.3 gallons of petrol. Estimate the miles per gallon, and decide before checking whether the estimate is high or low.
**Answer:** Estimate 50 mpg; exact 43.5 mpg (1 d.p.); an over-estimate
1. 187 rounds to 200 and 4.3 rounds to 4.
2. Numerator up, divisor down, so the estimate must be high.
3. 200 ÷ 4 = 50 mpg.
4. Exact: 187 ÷ 4.3 = 43.488…
5. The estimate is about 6.5 mpg generous — enough to strand you if you planned a journey on it.
### Question 10
Estimate (0.052 × 396) ÷ 0.021.
**Answer:** Estimate 1000; exact 980.6 (1 d.p.); an over-estimate
1. 0.052 → 0.05, 396 → 400, 0.021 → 0.02.
2. 0.05 × 400 = 20, and 20 ÷ 0.02 = 1000.
3. Exact: 0.052 × 396 = 20.592, and 20.592 ÷ 0.021 = 980.571…
4. Two of the three roundings push upwards: 396 raised, and the divisor 0.021 lowered.
5. Only 0.052 → 0.05 pushes down, so the estimate ends above the true value.
### Question 11
A rectangle measures 8.6 cm by 3.4 cm. Estimate its area to 1 significant figure and state the error.
**Answer:** Estimate 27 cm²; exact 29.24 cm²; under-estimate by 2.24 cm²
1. 8.6 rounds to 9 and 3.4 rounds to 3.
2. 9 × 3 = 27 cm².
3. Exact: 8.6 × 3.4 = 29.24 cm².
4. Raising 8.6 to 9 adds 0.4 × 3.4 = 1.36; lowering 3.4 to 3 removes 9 × 0.4 = 3.60.
5. 1.36 − 3.60 = −2.24, so the estimate is 2.24 cm² low.
### Question 12
Without calculating anything, say whether rounding to 1 significant figure will make 703 ÷ 0.68 come out too big or too small. Then estimate, and check.
**Answer:** Too small; estimate 1000; exact 1033.8 (1 d.p.)
1. 703 rounds down to 700; 0.68 rounds up to 0.7.
2. A smaller number divided by a larger divisor gives a smaller answer, so the estimate will be low.
3. 700 ÷ 0.7 = 1000.
4. Exact: 703 ÷ 0.68 = 1033.82…
5. The prediction was correct before any of the division was carried out.
## Questions
### What does rounding 0.048 to 1 significant figure give?
0.05. The first significant figure is the first non-zero digit, which is the 4 in the hundredths place, and the 8 after it rounds that 4 up to 5. Answers of 0.0 and 0.1 both come from counting decimal places instead, and both are out by a factor of ten or more.
### Can an estimate ever come out exactly right?
Yes, when one rounding gains as much as another loses. It is coincidence rather than a sign of good technique, and it does not license using the estimate as the exact answer. If a question asks for both, the exact working still has to be shown separately.
### My child gets the estimate right but the exact answer wrong. Is that a problem?
It is a useful diagnosis rather than a worry. A correct estimate shows the size of the answer is understood, so the marks are being lost in the written method — a misaligned column, a dropped carry, a decimal point in the wrong place. Those are far quicker to fix than missing number sense.
### How close does an estimate have to be to count as correct?
There is no percentage tolerance to hit. Credit goes to the method: round each number to one significant figure, then carry out that calculation correctly. An estimate of 800 for 38 × 21 does the job; 798 does not, because it shows the full multiplication was done and then relabelled.
---
Published by Learning Loft Institute, Lahore, Pakistan. Canonical HTML: https://www.learningloftinstitute.com/practice/estimation-and-checking-practice-questions. Site brief for models: https://www.learningloftinstitute.com/llms.txt.