AI generatedNumberGCSE Higher

Justifying a degree of accuracy

Compare the rounded lower and upper results.

  • Write the original error intervals before calculating. Keep the bounds exact.
  • Choose the combination of bounds that makes the result smallest or largest. The direction matters for subtraction and division.
  • Round only at the end. A stated upper bound need not be an attainable value.

Example 1

= 50.00 and = 200.00, each correct to 2 d.. To how many decimal places (up to 4) can be stated reliably?

Lower boundUse the smallest numerator and largest denominator.
Upper boundUse the largest numerator and smallest denominator.
Bound valuesCompare how both bounds round; keep only the places that agree.
, reliable to 4 decimal places.

Example 2

= 51.00 and = 201.00, each correct to 2 d.. To how many decimal places (up to 4) can be stated reliably?

Lower boundUse the smallest numerator and largest denominator.
Upper boundUse the largest numerator and smallest denominator.
Bound valuesCompare how both bounds round; keep only the places that agree.
, reliable to 3 decimal places.

Your turn

Question 1

= 52.00 and = 202.00, each correct to 2 d.. To how many decimal places (up to 4) can be stated reliably?

Check answer
Lower boundUse the smallest numerator and largest denominator.
Upper boundUse the largest numerator and smallest denominator.
Bound valuesCompare how both bounds round; keep only the places that agree.
, reliable to 3 decimal places.
Question 2

= 53.00 and = 203.00, each correct to 2 d.. To how many decimal places (up to 4) can be stated reliably?

Check answer
Lower boundUse the smallest numerator and largest denominator.
Upper boundUse the largest numerator and smallest denominator.
Bound valuesCompare how both bounds round; keep only the places that agree.
, reliable to 4 decimal places.
Question 3

= 54.00 and = 204.00, each correct to 2 d.. To how many decimal places (up to 4) can be stated reliably?

Check answer
Lower boundUse the smallest numerator and largest denominator.
Upper boundUse the largest numerator and smallest denominator.
Bound valuesCompare how both bounds round; keep only the places that agree.
, reliable to 4 decimal places.
Question 4

= 55.00 and = 205.00, each correct to 2 d.. To how many decimal places (up to 4) can be stated reliably?

Check answer
Lower boundUse the smallest numerator and largest denominator.
Upper boundUse the largest numerator and smallest denominator.
Bound valuesCompare how both bounds round; keep only the places that agree.
, reliable to 4 decimal places.
Question 5

= 56.00 and = 206.00, each correct to 2 d.. To how many decimal places (up to 4) can be stated reliably?

Check answer
Lower boundUse the smallest numerator and largest denominator.
Upper boundUse the largest numerator and smallest denominator.
Bound valuesCompare how both bounds round; keep only the places that agree.
, reliable to 3 decimal places.
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