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Rounding and Approximation

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Rounding and Approximation

Summary: Rounding simplifies numbers while keeping them close to the original value. Key methods include rounding to decimal places, significant figures, and the nearest 10/100/1000, plus estimation by rounding. Tags: concepts math y7 rounding approximation Created: 2026-05-30 Last Updated: 2026-05-30

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Rounding to the Nearest 10, 100, or 1000

To round a number, look at the digit immediately to the right of the place value you are rounding to:

  • If the next digit is 5 or more: round up
  • If the next digit is 4 or less: round down (keep the same)
Examples:
347 to nearest 10 → the 4 is followed by 7 (≥5), so round up → 350
2847 to nearest 100 → the 8 is followed by 4 (<5), so round down → 2800
7621 to nearest 1000 → the 7 is followed by 6 (≥5), so round up → 8000

Rounding to Decimal Places

Rounding to a specific number of decimal places follows the same principle: look at the digit one place beyond your target.

Examples:
3.14159 to 2 dp → look at the third decimal (1) which is <5 → 3.14
7.486 to 1 dp → look at the second decimal (8) which is ≥5 → 7.5
0.095 to 2 dp → look at the third decimal (5) which is ≥5 → 0.10

Note that 0.10 is written with the trailing zero to show it is accurate to 2 decimal places.

Rounding to Significant Figures

Significant figures count from the first non-zero digit. Leading zeros are not significant.

Rules for identifying significant figures:

  1. All non-zero digits are significant
  2. Zeros between non-zero digits are significant
  3. Trailing zeros after a decimal point are significant
  4. Leading zeros are NOT significant
Examples:
4628 to 1 sf → first digit is 4, next is 6 (≥5) → 5000
0.00582 to 1 sf → first non-zero is 5, next is 8 (≥5) → 0.006
37.49 to 2 sf → first two: 3, 7. Next is 4 (<5) → 37

Estimation

Estimation uses rounded numbers to find an approximate answer quickly. This is useful for checking whether a calculated answer is reasonable.

Method:

  1. Round each number in the calculation to 1 significant figure
  2. Perform the simplified calculation
Example: Estimate 48 × 31. Round 48 → 50 and 31 → 30. 50 × 30 = 1500. (The exact answer is 1488, so 1500 is a good estimate.)

Error Intervals (Bounds)

When a number has been rounded, the original value could have been anywhere within a certain range. The lower bound is the smallest possible original value. The upper bound is the largest possible original value.

For a measurement rounded to a given unit, the error interval is ± half of that unit.

Example: A length is given as 6.3 cm to 1 decimal place. Lower bound = 6.25 cm, Upper bound = 6.35 cm. The true length is somewhere in the interval 6.25 ≤ x < 6.35.

Key Points to Remember

  • Always read the question carefully to identify which type of rounding is required
  • “To 2 dp” means to 2 decimal places
  • “To 1 sf” means to 1 significant figure
  • Rounding up may cause a cascade (e.g. 3.996 → 4.0 to 1 dp)
  • Estimation is a powerful way to check if an answer makes sense

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