GCSE Estimation and checking Practice Questions

Free GCSE Estimation and checking practice questions with full step-by-step worked solutions. Covers rounding to 1 s.f., decimals, estimating, multiplication. Practise exam-style problems and check your method.

rounding to 1 s.f.decimalsestimatingmultiplicationadditionsubtraction
GCSE Foundation70 questionsStep-by-step solutions
Question 1
1 markeasy
Round 6868 to 1 significant figure.
Show worked solution

Worked solution

  1. Find the first significant figure

    6868

    The first significant figure of 68 is the 6, in the tens column.

  2. Look at the next digit

    68‾6\underline{8}

    The next digit is 8. Since 8 ≥ 5, round the tens digit up.

  3. Write the rounded number

    68≈7068 \approx 70

    6 tens becomes 7 tens and the units digit becomes 0, so 68 ≈ 70.

Answer
7070
Question 2
2 markseasy
Estimate 99\sqrt{99}. Give your answer to the nearest whole number.
Show worked solution

Worked solution

  1. Find nearby square numbers

    81<99<10081 < 99 < 100

    99 lies between the square numbers 81 and 100.

  2. Take the square roots

    81=9, 100=10\sqrt{81} = 9,\ \sqrt{100} = 10

    So √99 lies between 9 and 10.

  3. Choose the closer value

    99≈100⇒99≈1099 \approx 100 \Rightarrow \sqrt{99} \approx 10

    99 is much closer to 100 than to 81, so √99 ≈ 10.

Answer
1010
Question 3
2 marksintermediate
Estimate the value of 48×2.1\sqrt{48 \times 2.1}.
Show worked solution

Worked solution

  1. Round the first number

    48≈5048 \approx 50

    48 to 1 s.f. is 50.

  2. Round the second number

    2.1≈22.1 \approx 2

    2.1 to 1 s.f. is 2.

  3. Rewrite the calculation

    50×2\sqrt{50 \times 2}

    Replace each number with its 1 s.f. value.

  4. Multiply inside the root

    50×2=10050 \times 2 = 100

    Work out the product under the root first.

  5. Take the square root

    100=10\sqrt{100} = 10

    100 is a square number.

  6. State the estimate

    ≈10\approx 10

    So the estimate is 10.

Answer
1010
Question 4
4 markshard
A stadium has 4242 rows, each with 388388 seats. Estimate the total number of seats.
Show worked solution

Worked solution

  1. Plan the estimate

    seats=rows×per row\text{seats} = \text{rows} \times \text{per row}

    Round each number to 1 s.f., then multiply.

  2. Round the number of rows

    42≈4042 \approx 40

    42 to 1 s.f. is 40.

  3. Round the seats per row

    388≈400388 \approx 400

    388 to 1 s.f. is 400.

  4. Rewrite the calculation

    40×40040 \times 400

    Substitute the rounded values.

  5. Multiply

    40×400=1600040 \times 400 = 16000

    4×4=164 \times 4 = 16, then attach the zeros.

  6. Attach the units

    16000 seats16000 \text{ seats}

    The answer counts seats.

  7. Sense-check

    40×400=1600040 \times 400 = 16000

    A sensible size for a stadium.

  8. Compare the rounding

    40<42, 400>38840 < 42,\ 400 > 388

    One number down, one up.

  9. Reflect

    directions partly cancel\text{directions partly cancel}

    So 16000 is close to the true total.

  10. State the estimate

    ≈16000 seats\approx 16000 \text{ seats}

    So there are about 16000 seats.

Answer
16000 seats16000 \text{ seats}
Question 5
6 markschallenging
Estimate the value of 104×390.021\dfrac{\sqrt{104} \times 39}{0.021}.
Show worked solution

Worked solution

  1. Plan the estimate

    root first, then round\text{root first, then round}

    Estimate the square root, then round the other numbers.

  2. Round the number under the root

    104≈100104 \approx 100

    104 to 1 s.f. is 100.

  3. Take the square root

    100=10\sqrt{100} = 10

    So √104 ≈ 10.

  4. Round 39

    39≈4039 \approx 40

    To 1 s.f. this is 40.

  5. Round 0.021

    0.021≈0.020.021 \approx 0.02

    To 1 s.f. this is 0.02.

  6. Rewrite the calculation

    10×400.02\frac{10 \times 40}{0.02}

    Substitute the rounded values.

  7. Work out the numerator

    10×40=40010 \times 40 = 400

    Multiply the top first.

  8. Rewrite the fraction

    4000.02\frac{400}{0.02}

    Now divide by the decimal.

  9. Divide by a decimal

    ÷0.02=×50\div 0.02 = \times 50

    Dividing by 0.02 is the same as multiplying by 50.

  10. Work it out

    400×50=20000400 \times 50 = 20000

    So the estimate is 20000.

  11. Check the size

    0.02×20000=4000.02 \times 20000 = 400

    Reversing the division returns 400.

  12. Note the effect

    0.02<10.02 < 1

    Dividing by a small decimal greatly increases the value.

  13. Sense-check the root

    102=100≈10410^{2} = 100 \approx 104

    The square root estimate is reliable.

  14. Reflect

    answer in the tens of thousands\text{answer in the tens of thousands}

    A sensible size given the small divisor.

  15. State the estimate

    ≈20000\approx 20000

    So the estimate is 20000.

Answer
2000020000

Unlock 65 more Estimation and checking questions

Create a free account to work through every GCSE Estimation and checking question with instant step-by-step worked solutions, progress tracking and interactive lessons.

  • Full worked solutions for every question
  • Interactive lessons and instant feedback
  • Track your mastery across every topic
Create a Free Account

No card required · Free forever

More Estimation and checking practice

Hard QuestionsWorked Solutions

Related Number topics

Upper and lower boundsError intervalsEstimating powers and rootsExact calculationFactors, multiples and primesFDP equivalence