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 11 significant figure.
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Worked solution

  1. Find the first significant figure

    6868

    The first significant figure of 6868 is the 66, 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

    66 tens becomes 77 tens and the units digit becomes 00, so 6868 ≈ 7070.

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

  1. Find nearby square numbers

    81<99<10081 < 99 < 100

    9999 lies between the square numbers 8181 and 100100.

  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}.
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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

    100100 is a square number.

  6. State the estimate

    ≈10\approx 10

    So the estimate is 1010.

Answer
1010
Question 4
4 markshard
A stadium has 4242 rows, each with 388388 seats. Estimate the total number of seats.
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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 1600016000 is close to the true total.

  10. State the estimate

    ≈16000 seats\approx 16000 \text{ seats}

    So there are about 1600016000 seats.

Answer
16000 seats16000 \text{ seats}
Question 5
6 markschallenging
Estimate the value of 104×390.021\dfrac{\sqrt{104} \times 39}{0.021}.
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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 3939

    39≈4039 \approx 40

    To 1 s.f. this is 40.

  5. Round 0.0210.021

    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 0.020.02 is the same as multiplying by 5050.

  10. Work it out

    400×50=20000400 \times 50 = 20000

    So the estimate is 2000020000.

  11. Check the size

    0.02×20000=4000.02 \times 20000 = 400

    Reversing the division returns 400400.

  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 2000020000.

Answer
2000020000

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