Rounding & Estimation

Spec reference: Number - Rounding and approximation
Key idea: Round numbers to decimal places and significant figures; estimate answers to calculations.

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Rounding to decimal places (d.p.)

1. Identify the digit in the position you are rounding to
2. Look at the next digit (the one to the right)
3. If it is 5 or more, round up. If it is 4 or less, round down (keep the digit the same)

Example

Round 3.7461 to 2 decimal places.

The digit in the 2nd d.p. position is 4.
The next digit is 6 (>= 5), so round up.

$$3.7461\approx \boxed{{\displaystyle 3.75}}$$

Example

Round 0.08349 to 3 decimal places.

The digit in the 3rd d.p. position is 3.
The next digit is 4 (< 5), so round down.

$$0.08349\approx \boxed{{\displaystyle 0.083}}$$

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Rounding to significant figures (s.f.)

The first significant figure is the first non-zero digit.

1. Count to the required significant figure
2. Apply the same rounding rule as above
3. Replace digits after the rounded position with zeros if they are before the decimal point

Example

Round 47,382 to 2 significant figures.

The 2nd significant figure is 7.
The next digit is 3 (< 5), so round down.

$$\mathrm{47,382}\approx \boxed{{\displaystyle \mathrm{47,000}}}$$

Example

Round 0.006842 to 2 significant figures.

The 1st significant figure is 6 (first non-zero).
The 2nd is 8.
The next digit is 4 (< 5), so round down.

$$0.006842\approx \boxed{{\displaystyle 0.0068}}$$

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Estimation

To estimate, round each number to 1 significant figure, then calculate.

Example

Estimate ${\displaystyle \frac{38.4\times 5.92}{0.21}}$

Round each value:

$$\frac{40\times 6}{0.2}=\frac{240}{0.2}=\boxed{{\displaystyle 1200}}$$

TIP

Estimation is useful to check whether a calculator answer is sensible.

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Truncation

Truncation means cutting off digits after a certain point, without rounding up.

Example

Truncate 4.897 to 2 decimal places.

Simply remove digits after the 2nd d.p.:

$$4.897\to \boxed{{\displaystyle 4.89}}$$

Note: rounding gives 4.90, but truncation gives 4.89.

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Exam tips

Watch out for

• Trailing zeros matter: 3.50 to 2 d.p. must be written as 3.50, not 3.5
• For significant figures, zeros between non-zero digits are significant: 3,007 has 4 s.f.
• Leading zeros are not significant: 0.0045 has 2 s.f.

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Test Yourself

Question 1 of 5

Round 4.7836 to 2 decimal places