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Degree of accuracy

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Pearson Edexcel International GCSE Mathematics A (4MA1)

Degree of Accuracy

The big idea: Every rounded number stands for a range of values. Rounding picks one value from the range; bounds give its two ends; and Higher bounds questions choose the ends that make an answer as big or as small as possible.

Summary — What This Chapter Covers

Round integers to the nearest 10, 100, 1000 …
Round to a given number of decimal places or significant figures.
Find the lower and upper bounds of a value given to a degree of accuracy: ± half the unit.
Estimate a calculation by rounding every number to 1 significant figure.
Higher: solve problems with bounds, choosing upper or lower bounds to maximise or minimise the result.

1. Rounding Integers to a Power of 10

Foundation & Higher

Nearest 10, 100, 1000

Look at the digit immediately to the right of the place you are rounding to. If it is 5 or more, round up; otherwise round down. Keep the place value with zeros.

Practice Question 1

Round 48 362 to the nearest (a) 10 (b) 100 (c) 1000.

2. Significant Figures and Decimal Places

Foundation & Higher

Count from the first non-zero digit

Decimal places count digits after the decimal point. Significant figures start at the first non-zero digit. Zeros at the start of a decimal are never significant; zeros between other digits always are.

Worked Example

Round (a) 37.4682 to 2 decimal places and to 3 significant figures (b) 0.0040762 to 3 significant figures (c) 6049 to 2 significant figures.

4MA1 default

If a question does not say how to round, give an exact answer or 3 significant figures, and angles to 1 decimal place. Write down the full calculator value first, then round.

3. Upper and Lower Bounds

Foundation & Higher

Half a unit each way

A measurement given to a degree of accuracy could be anywhere in a range. The bounds are half of the rounding unit below and above the given value.

Bounds given to the nearest u: value − u/2 ≤ x < value + u/2

Worked Example

Write down the lower and upper bounds of (a) a length of 12 cm, to the nearest cm (b) a mass of 3.7 kg, to 1 decimal place (c) a crowd of 400 people, to the nearest 100.

Practice Question 2

The time for a race is 48.3 seconds, correct to the nearest 0.1 second. Write down the error interval for the time t.

4. Estimation

Foundation & Higher

Round each number to 1 significant figure

To estimate, round every number to 1 significant figure and work out the simpler calculation. Show the rounded values, since that is where the method mark is.

Worked Example

Work out an estimate for (48.7 × 3.12) ÷ 0.196

Practice Question 3

By rounding each number to 1 significant figure, estimate (6.12 × 39.4) ÷ 0.48

5. Problems Using Upper and Lower Bounds

Higher tier

Choose the bound that pushes the answer the right way

Work out the bounds of each value first. Then decide which combination makes the result largest or smallest.

Combining bounds

Worked Example

Practice Question 4

Memorise

Bounds

± half the unit of accuracy. Lower ≤ x < upper.

Significant figures

Estimation

Common Mistakes

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Degree of accuracy

Degree of Accuracy

Nearest 10, 100, 1000

Count from the first non-zero digit

Half a unit each way

Round each number to 1 significant figure

Choose the bound that pushes the answer the right way

Bounds

Significant figures

Estimation

Past papers that test Degree of accuracy

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