Error intervals Worked Solutions — GCSE Maths

Fully worked, step-by-step solutions to GCSE Error intervals questions. See exactly how to solve problems on error intervals, rounding to nearest 10, rounding to nearest 100, rounding to nearest integer.

error intervalsrounding to nearest 10rounding to nearest 100rounding to nearest integerrounding to 1 dptruncation
GCSE Foundation70 questionsStep-by-step solutions
Question 1
1 markeasy
A number xx is 7070 when rounded to the nearest 1010. Write down the error interval for xx.

Worked solution

  1. Interpret the rounded value

    x≈70x \approx 70

    xx has been rounded to the nearest 10, so it lies in an interval around 7070.

  2. Find the lower and upper bounds

    70−5=65and70+5=7570 - 5 = 65 \quad\text{and}\quad 70 + 5 = 75

    The boundaries lie exactly half a unit (55) either side of 7070.

  3. Write the error interval

    65≤x<7565 \le x < 75

    Any value from 6565 up to 7070 rounds to 7070, so the lower bound 6565 is included. A value of 7575 would round up to the next value, so 7575 is not included.

Answer
65≤x<7565 \le x < 75
Question 2
1 markeasy
A number xx is 200200 when rounded to the nearest 100100. Write down the error interval for xx.

Worked solution

  1. Interpret the rounded value

    x≈200x \approx 200

    xx has been rounded to the nearest 100, so it lies in an interval around 200200.

  2. Find the lower and upper bounds

    200−50=150and200+50=250200 - 50 = 150 \quad\text{and}\quad 200 + 50 = 250

    The boundaries lie exactly half a unit (5050) either side of 200200.

  3. Write the error interval

    150≤x<250150 \le x < 250

    Any value from 150150 up to 200200 rounds to 200200, so the lower bound 150150 is included. A value of 250250 would round up to the next value, so 250250 is not included.

Answer
150≤x<250150 \le x < 250
Question 3
1 markeasy
A number xx is 88 when rounded to the nearest whole number. Write down the error interval for xx.

Worked solution

  1. Interpret the rounded value

    x≈8x \approx 8

    xx has been rounded to the nearest whole number, so it lies in an interval around 88.

  2. Find the lower and upper bounds

    8−0.5=7.5and8+0.5=8.58 - 0.5 = 7.5 \quad\text{and}\quad 8 + 0.5 = 8.5

    The boundaries lie exactly half a unit (0.50.5) either side of 88.

  3. Write the error interval

    7.5≤x<8.57.5 \le x < 8.5

    Any value from 7.57.5 up to 88 rounds to 88, so the lower bound 7.57.5 is included. A value of 8.58.5 would round up to the next value, so 8.58.5 is not included.

Answer
7.5≤x<8.57.5 \le x < 8.5
Question 4
2 markseasy
The number xx rounds to 4.64.6 to 11 decimal place. Write down the error interval for xx.

Worked solution

  1. Interpret the rounded value

    x≈4.6x \approx 4.6

    xx has been rounded to 1 decimal place, so it lies in an interval around 4.64.6.

  2. Find the lower and upper bounds

    4.6−0.05=4.55and4.6+0.05=4.654.6 - 0.05 = 4.55 \quad\text{and}\quad 4.6 + 0.05 = 4.65

    The boundaries lie exactly half a unit (0.050.05) either side of 4.64.6.

  3. Write the error interval

    4.55≤x<4.654.55 \le x < 4.65

    Any value from 4.554.55 up to 4.64.6 rounds to 4.64.6, so the lower bound 4.554.55 is included. A value of 4.654.65 would round up to the next value, so 4.654.65 is not included.

Answer
4.55≤x<4.654.55 \le x < 4.65
Question 5
1 markeasy
A number xx is 1212 when rounded to the nearest whole number. Write down the error interval for xx.

Worked solution

  1. Interpret the rounded value

    x≈12x \approx 12

    xx has been rounded to the nearest whole number, so it lies in an interval around 1212.

  2. Find the lower and upper bounds

    12−0.5=11.5and12+0.5=12.512 - 0.5 = 11.5 \quad\text{and}\quad 12 + 0.5 = 12.5

    The boundaries lie exactly half a unit (0.50.5) either side of 1212.

  3. Write the error interval

    11.5≤x<12.511.5 \le x < 12.5

    Any value from 11.511.5 up to 1212 rounds to 1212, so the lower bound 11.511.5 is included. A value of 12.512.5 would round up to the next value, so 12.512.5 is not included.

Answer
11.5≤x<12.511.5 \le x < 12.5

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