What is the degree of accuracy in mathematics?

In mathematics, particularly in the context of the Edexcel IGCSE curriculum, the degree of accuracy refers to the precision with which a number is expressed. It indicates how close a measured or calculated value is to the true value, often specified by the number of significant figures or decimal places.

How do you determine the degree of accuracy for a given number?

To determine the degree of accuracy for a number, you need to identify how it is rounded. This could be to a certain number of decimal places or significant figures. For example, if a number is rounded to two decimal places, its degree of accuracy is to the nearest hundredth.

Why is the degree of accuracy important in the Edexcel IGCSE Mathematics exam?

The degree of accuracy is crucial in the Edexcel IGCSE Mathematics exam because it ensures that answers are precise and consistent with the problem's requirements. It helps in minimizing errors and provides clarity in calculations, which is essential for achieving accurate results.

What is the difference between significant figures and decimal places in terms of degree of accuracy?

Significant figures refer to the total number of meaningful digits in a number, starting from the first non-zero digit. Decimal places, on the other hand, count the number of digits to the right of the decimal point. Both are used to express the degree of accuracy, but they focus on different aspects of a number's precision.

How can rounding affect the degree of accuracy in calculations?

Rounding can affect the degree of accuracy by altering the precision of a number. When a number is rounded, it is adjusted to a specified degree of accuracy, such as a certain number of decimal places or significant figures. This can lead to small discrepancies in calculations, especially when multiple rounded numbers are used in a sequence of operations.

Why is "Counting leading zeros as significant figures" a common mistake in Degree of Accuracy?

Why it happens: All digits look meaningful. How to avoid it: Leading zeros (before the first non-zero digit) are NOT significant. 0.0067 has 2 s.f. (6 and 7).

Why is "Using the rounding unit (not HALF) for bounds" a common mistake in Degree of Accuracy?

Why it happens: Quick guess. How to avoid it: ALWAYS halve the rounding unit. For 1 d.p. (0.1): 0.05. For nearest 10: 5.

Why is "Computing $\min(a-b)$ as $\min(a) - \min(b)$" a common mistake in Degree of Accuracy?

Why it happens: Both operations use 'min', so students apply consistent logic. How to avoid it: Subtraction REVERSES one bound: (a-b) = (a) - (b). Imagine a smallest and b largest — biggest gap to subtract = smallest result. Source: 4MA1/2H May/Jun 2024 — examiner report Q19

Why is "Computing $\max(a/b)$ as $\max(a) / \max(b)$" a common mistake in Degree of Accuracy?

Why it happens: Same logic error. How to avoid it: Division: (a/b) = (a) / (b). Big top, small bottom = biggest result. Same logic for (a/b) = (a) / (b).

Why is "Rounding $0.65$ to $1$ d.p. as $0.6$" a common mistake in Degree of Accuracy?

Why it happens: Confusion about exactly 5. How to avoid it: Edexcel uses 'round HALF UP': exactly 5 rounds up. 0.65 → 0.7 to 1 d.p.

Numbers and the Number SystemEdexcel IGCSE Mathematics (4MA1)

Degree of Accuracy

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Degree of Accuracy Study Notes — Edexcel IGCSE 4MA1 Higher Tier (2026 onwards)

Rounding, significant figures, and bounds. The technique behind A* answers when measurements have been rounded — used in any 'find the largest/smallest possible' question.

What you’ll learn

Mapped to the Cambridge IGCSE 4MA1 syllabus (2026 onwards).

1.10 — Round to a given number of decimal places or significant figures.
1.10 — Identify upper and lower bounds for measurements.
1.10 — Use bounds in calculations (multiplication, division, subtraction).

Rounding to d.p. and s.f.

d.p. counts after the decimal. s.f. counts from the first non-zero digit.

Decimal places (d.p.). Count digits AFTER the decimal point.

$3.14159$ to $2$ d.p.: look at 3rd d.p. ( $1$ ) → round down → $3.14$ .
$3.14159$ to $3$ d.p.: look at 4th d.p. ( $5$ ) → round UP → $3.142$ .

Significant figures (s.f.). Start counting at the FIRST non-zero digit.

$0.0067$ has $2$ s.f. ( $6, 7$ ).
$0.0670$ has $3$ s.f. ( $6, 7, 0$ — trailing zero after decimal IS significant).
$5670$ has $3$ s.f. (trailing zeros in integers are AMBIGUOUS — usually $4$ or $3$ ).
$5670.0$ has $5$ s.f. (decimal forces all trailing zeros to count).

Rules:

Leading zeros (before first non-zero) are NEVER significant.
Zeros between non-zero digits ARE significant. ( $304$ has $3$ s.f.)
Trailing zeros after a decimal ARE significant. ( $30.0$ has $3$ s.f.)
Trailing zeros in integers are ambiguous — treat per context.

Round half up. When the digit being rounded is exactly $5$ , round UP.

$0.65$ to $1$ d.p. → $0.7$ .
$1.85$ to $1$ d.p. → $1.9$ .

Worked qualitative. Why is $0.0067$ said to have $2$ s.f., not $5$ ?

Significant figures convey ACTUAL PRECISION, not how many digits are written.
The leading zeros just mark the place value (telling us this is a small number) — they don't add precision.
Two non-zero digits = two significant figures.

Edexcel tip. Always state both numbers when rounding: 'Look at the next digit ( $X$ ); since $X \ge 5$ / $X < 5$ , round up/down'.

d.p. counts after decimal.
s.f. starts from first non-zero.
Leading zeros: not significant.
Trailing zeros after decimal: significant.
Half UP for exact $5$ .

Upper and lower bounds — single value

When a value is rounded, the true value lies in a half-interval around it.

The rule: A value rounded to a unit $u$ lies within $\pm \dfrac{u}{2}$ of the stated value.

Stated as	Rounding unit $u$	Half-unit	Bounds
$7.4$ ( $1$ d.p.)	$0.1$	$0.05$	$[7.35, 7.45)$
$7.40$ ( $2$ d.p.)	$0.01$	$0.005$	$[7.395, 7.405)$
$250$ (nearest $10$ )	$10$	$5$	$[245, 255)$
$250$ (nearest $50$ )	$50$	$25$	$[225, 275)$
$5.6$ ( $2$ s.f.)	$0.1$	$0.05$	$[5.55, 5.65)$

Notation: square bracket $[$ for inclusive (lower bound), parenthesis $)$ for exclusive (upper bound). Conventionally:

LOWER bound is INCLUDED.
UPPER bound is EXCLUDED (because $7.45$ would round UP to $7.5$ ).

Worked example. A measurement is given as $52$ kg to the nearest kg. Find bounds.

$u = 1$ kg. Half-unit $= 0.5$ kg.

Lower bound = $51.5$ kg. Upper bound = $52.5$ kg.

Worked qualitative. Why is the upper bound 'excluded'?

$52.5$ would round UP to $53$ (because of round half up).
So if the original value was exactly $52.5$ , it would be reported as $53$ , not $52$ .
The actual range of values reported as $52$ is $[51.5, 52.5)$ .

Edexcel tip. State the rounding unit and halve it explicitly. 'Rounded to $1$ d.p., so half-unit is $0.05$ .' This earns the M1 mark.

Bounds = stated value $\pm u/2$ .
Lower bound INCLUDED (round-up convention).
Upper bound EXCLUDED.
Always state $u$ explicitly.

Bounds in calculations

Different operations need different combinations of upper and lower bounds.

Why this matters. When computing $a \times b$ where both are rounded, the answer has its own range. To find the range, combine the bounds correctly.

Addition. Both bounds add naturally:

$UB(a + b) = UB(a) + UB(b)$ .
$LB(a + b) = LB(a) + LB(b)$ .

Subtraction. REVERSE one bound:

$UB(a - b) = UB(a) - LB(b)$ .
$LB(a - b) = LB(a) - UB(b)$ .

(Think: biggest gap when first is largest, second is smallest.)

Multiplication. Both same direction (for positive values):

$UB(a \times b) = UB(a) \times UB(b)$ .
$LB(a \times b) = LB(a) \times LB(b)$ .

Division. Mixed (for positive values):

$UB(a \div b) = UB(a) \div LB(b)$ .
$LB(a \div b) = LB(a) \div UB(b)$ .

Memory aid.

Want big? Make top big, bottom small.
Want small? Make top small, bottom big.

Worked example. $a = 8.2$ ( $1$ d.p.), $b = 4.5$ ( $1$ d.p.). Find UB and LB of $a/b$ .

Bounds: $a \in [8.15, 8.25]$ , $b \in [4.45, 4.55]$ .

$UB(a/b) = 8.25 / 4.45 = 1.853\ldots$
$LB(a/b) = 8.15 / 4.55 = 1.791\ldots$

So $a/b \in [1.791, 1.854]$ approximately.

Worked qualitative. Why does division use 'big over small' for the upper bound?

Bigger numerator → bigger answer.
Smaller denominator → bigger answer.
For maximum, want both effects: max numerator, min denominator.

Edexcel tip. Set up bounds explicitly: $a \in [\ldots, \ldots]$ , $b \in [\ldots, \ldots]$ . Then choose the right combination. Mark schemes credit each bound calculation step.

Addition: same direction.
Subtraction: reverse one.
Multiplication: same direction.
Division: max top, min bottom.

How it’s examined

Degree of accuracy appears Paper 1H (rounding, 2-3 marks) AND Paper 2H (bounds in calculations, 4-6 marks). Examiner reports flag (1) confusing leading zeros vs significant trailing zeros, (2) using $u$ (not $u/2$ ) for bounds, and (3) wrong bound combinations in division and subtraction.

Sources: Pearson Edexcel International GCSE Mathematics A 4MA1 specification (2026 onwards); 4MA1 Examiner Reports — Jan and May/Jun 2022-2024 series; Past Papers — 4MA1/2H May/Jun 2024. Last reviewed 2026-05-07.

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Step-by-step worked examples — Degree of Accuracy

Step-by-step solutions to past-paper-style questions on degree of accuracy, written exactly the way a tutor would explain them at the board.

1Round to a given accuracy
Foundation• rounding
Question
Round $0.06743$ to (a) $1$ d.p., (b) $2$ s.f., (c) $3$ s.f.
Step-by-step solution
1. Step 1
  (a) $1$ d.p.: look at the 2nd decimal place ( $6$ ) — round up. $0.06743 \to 0.1$ .
2. Step 2
  (b) $2$ s.f.: leading zeros don't count. The first two significant figures are $6$ and $7$ . Look at the next ( $4$ ) — round down. $0.06743 \to 0.067$ .
3. Step 3
  (c) $3$ s.f.: include $4$ . Next digit is $3$ — round down. $0.06743 \to 0.0674$ .
Answer
(a) $0.1$ (b) $0.067$ (c) $0.0674$
Examiner tip
Significant figures count from the FIRST non-zero digit. Leading zeros are not significant. Trailing zeros after a decimal ARE significant.
2Find upper and lower bounds
Higher• bounds
Question
A length is measured as $7.4$ cm to $1$ d.p. Find the upper and lower bounds.
Step-by-step solution
1. Step 1
  Half of the smallest unit ( $0.1$ ) is $0.05$ .
2. Step 2
  Lower bound: $7.4 - 0.05 = 7.35$ cm.
3. Step 3
  Upper bound: $7.4 + 0.05 = 7.45$ cm.
Answer
Lower bound $7.35$ cm; upper bound $7.45$ cm.
Examiner tip
ALWAYS halve the rounding unit. For $1$ d.p. ( $0.1$ ): bounds $\pm 0.05$ . For $2$ s.f.: bounds $\pm$ half of last sig fig place value.
3Bounds with multiplication
Higher• Adapted from 4MA1/2H May/Jun 2024 Q19• bounds, multiplication
Question
$a = 8.2$ to $1$ d.p., $b = 4.5$ to $1$ d.p. Find the upper bound of $a \times b$ .
Step-by-step solution
1. Step 1
  Bounds: $a \in [8.15, 8.25]$ , $b \in [4.45, 4.55]$ .
2. Step 2
  For multiplication, max product = max × max:
  $(\text{UB of}\ a)\times(\text{UB of}\ b) = 8.25 \times 4.55$
3. Step 3
  Compute: $8.25 \times 4.55 = 37.5375$ .
Answer
Upper bound = $37.5375$
Examiner tip
For multiplication: max × max for upper bound; min × min for lower bound. For division: max ÷ min for upper bound; min ÷ max for lower bound.
4Bounds with subtraction
Higher• bounds, subtraction
Question
$a = 12.6$ to $1$ d.p., $b = 5.3$ to $1$ d.p. Find the lower bound of $a - b$ .
Step-by-step solution
1. Step 1
  Bounds: $a \in [12.55, 12.65]$ , $b \in [5.25, 5.35]$ .
2. Step 2
  For SUBTRACTION, MIN of $a - b$ uses MIN of $a$ and MAX of $b$ :
  $\min(a - b) = \min(a) - \max(b) = 12.55 - 5.35 = 7.2$
Answer
Lower bound = $7.2$
Examiner tip
Subtraction is the trickiest case. Lower bound: smallest $a$ minus largest $b$ . Upper bound: largest $a$ minus smallest $b$ . Many students get this WRONG by 'min minus min'.
5Truncate vs round
Foundation• truncate
Question
Truncate $\pi = 3.14159\ldots$ to $3$ decimal places. Compare with rounding to $3$ d.p.
Step-by-step solution
1. Step 1
  TRUNCATING: just chop off after $3$ d.p. → $3.141$ .
2. Step 2
  ROUNDING: look at next digit ( $5$ ) → round up → $3.142$ .
Answer
Truncate: $3.141$ . Round: $3.142$ .
Examiner tip
Edexcel rarely asks for truncation explicitly, but it's used in some money calculations. Always read the question carefully — 'round' and 'truncate' give different answers.

Key Formulae — Degree of Accuracy

The formulae you need to memorise for degree of accuracy on the Pearson Edexcel IGCSE 4MA1 paper, with every variable defined in plain English and a note on when to use it.

Bounds rule (rounded values)
$\text{If}\ x\ \text{is rounded to a unit}\ u,\ \text{then}\ x \in [x - u/2,\ x + u/2)$
$u$
the smallest place-value unit (e.g. $0.1$ for $1$ d.p., $1$ for nearest integer)
When to use
Whenever a value is given to a stated accuracy. Halve the rounding unit to get the half-interval.
Example
$7.4$ to $1$ d.p. ( $u = 0.1$ ): $x \in [7.35, 7.45)$ . $250$ to nearest $10$ ( $u = 10$ ): $x \in [245, 255)$ .
Bounds in arithmetic
$\text{Multiplication}: UB(ab) = UB(a) \cdot UB(b),\ LB(ab) = LB(a) \cdot LB(b)$
$UB, LB$
upper bound, lower bound
When to use
When computing max/min of expressions involving rounded values. Different operations need different combinations.
Example
Subtraction: $UB(a-b) = UB(a) - LB(b)$ . Division: $UB(a/b) = UB(a) / LB(b)$ .

Key Definitions and Keywords — Degree of Accuracy

Definitions to memorise and the exact keywords mark schemes credit for degree of accuracy answers — sharpened from recent examiner reports for the 2026 Pearson Edexcel IGCSE 4MA1 sitting.

Decimal places (d.p.)
Examiner keyword
The number of digits after the decimal point.
Example
$3.142$ has $3$ d.p.
Significant figures (s.f.)
Examiner keyword
Digits that carry meaning. Counting starts from the first non-zero digit. Leading zeros don't count; trailing zeros after the decimal DO count.
Example
$0.06743$ has $4$ s.f. (the digits $6, 7, 4, 3$ ).
Upper bound
Examiner keyword
The largest value that would round to the given measurement. Half the rounding unit ABOVE the stated value.
Example
$7.4$ to $1$ d.p. → upper bound $7.45$ .
Lower bound
Examiner keyword
The smallest value that would round to the given measurement. Half the rounding unit BELOW the stated value.
Example
$7.4$ to $1$ d.p. → lower bound $7.35$ .
Truncate
Discard digits beyond a chosen place. Doesn't round — just chops off.
Example
Truncate $3.789$ to $1$ d.p. → $3.7$ (NOT $3.8$ ).

Common Mistakes and Misconceptions — Degree of Accuracy

The traps other students keep falling into on degree of accuracy questions — taken from recent Pearson Edexcel IGCSE 4MA1 examiner reports and mark schemes — and how to avoid them.

✕Counting leading zeros as significant figures
Why it happens
All digits look meaningful.
How to avoid it
Leading zeros (before the first non-zero digit) are NOT significant. $0.0067$ has $2$ s.f. ( $6$ and $7$ ).
✕Using the rounding unit (not HALF) for bounds
Why it happens
Quick guess.
How to avoid it
ALWAYS halve the rounding unit. For $1$ d.p. ( $0.1$ ): $\pm 0.05$ . For nearest $10$ : $\pm 5$ .
✕Computing $\min(a-b)$ as $\min(a) - \min(b)$
4MA1/2H May/Jun 2024 — examiner report Q19
Why it happens
Both operations use 'min', so students apply consistent logic.
How to avoid it
Subtraction REVERSES one bound: $\min(a-b) = \min(a) - \max(b)$ . Imagine $a$ smallest and $b$ largest — biggest gap to subtract = smallest result.
✕Computing $\max(a/b)$ as $\max(a) / \max(b)$
Why it happens
Same logic error.
How to avoid it
Division: $\max(a/b) = \max(a) / \min(b)$ . Big top, small bottom = biggest result. Same logic for $\min(a/b) = \min(a) / \max(b)$ .
✕Rounding $0.65$ to $1$ d.p. as $0.6$
Why it happens
Confusion about exactly $5$ .
How to avoid it
Edexcel uses 'round HALF UP': exactly $5$ rounds up. $0.65$ → $0.7$ to $1$ d.p.

Practice questions

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Degree of Accuracy — frequently asked questions

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Degree of Accuracy

Short Study Notes in the form of Slides

Detailed Study Notes

What you’ll learn

How it’s examined

1Round to a given accuracy

2Find upper and lower bounds

3Bounds with multiplication

4Bounds with subtraction

5Truncate vs round

Bounds rule (rounded values)

Bounds in arithmetic

Decimal places (d.p.)

Significant figures (s.f.)

Upper bound

Lower bound

Truncate

✕Counting leading zeros as significant figures

✕Using the rounding unit (not HALF) for bounds

✕Computing min⁡(a−b)\min(a-b)min(a−b) as min⁡(a)−min⁡(b)\min(a) - \min(b)min(a)−min(b)

✕Computing max⁡(a/b)\max(a/b)max(a/b) as max⁡(a)/max⁡(b)\max(a) / \max(b)max(a)/max(b)

✕Rounding 0.650.650.65 to 111 d.p. as 0.60.60.6

Practice questions

Past paper style quiz

Assess your understanding

Video lesson

Degree of Accuracy — frequently asked questions

✕Computing $\min(a-b)$ as $\min(a) - \min(b)$

✕Computing $\max(a/b)$ as $\max(a) / \max(b)$

✕Rounding $0.65$ to $1$ d.p. as $0.6$