Estimation

2026 Syllabus Objectives

By the end of this topic, you should be able to:

  1. Round values to a specified degree of accuracy
  2. Make estimates for calculations involving numbers, quantities and measurements
  3. Round answers to a reasonable degree of accuracy in the context of a given problem
  4. Work with decimal places and significant figures (e.g., write 5764 correct to the nearest thousand; estimate 41.3 ÷ (9.79 × 0.765) by rounding each number to 1 significant figure)

What is Rounding and Why Do We Need It?

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In mathematics, we often work with numbers that have many digits or decimal places. Sometimes we don't need an exact answer—we just need a number that is "close enough" for the situation. This is where rounding comes in.

Rounding means changing a number to a simpler version that is approximately the same value. We round numbers to make them easier to work with, easier to remember, or more appropriate for the situation.

For example:

  • A calculator might show 3.6666666667, but we could round this to 3.7 or even just 4
  • A price of 24.99isessentially24.99 is essentially 25
  • A distance of 1,294 meters could be rounded to 1,300 meters or 1 kilometer

Rounding to Decimal Places

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Decimal places (written as d.p.) refers to the number of digits that appear to the right of the decimal point.

For example:

  • 3.185 has 3 decimal places
  • 0.21 has 2 decimal places
  • 0.3 has 1 decimal place

How to Round to Decimal Places

Follow these steps:

Step 1: Identify which decimal place you need to round to. This is your "target digit."

Step 2: Look at the digit immediately to the right of your target digit. This is your "deciding digit."

Step 3: Apply the rounding rule:

  • If the deciding digit is 5 or more → round UP (increase the target digit by 1)
  • If the deciding digit is less than 5 → round DOWN (keep the target digit the same)

Step 4: Remove all digits after your target digit. For decimal places, do not add extra zeros at the end.

Examples of Rounding to Decimal Places

Example 1: Round 64.839906 to 1 decimal place

  • Target digit: The first decimal place is 8
  • Deciding digit: The next digit is 3
  • Since 3 < 5, we round down
  • Answer: 64.8 (1 d.p.)

Example 2: Round 64.839906 to 3 decimal places

  • Target digit: The third decimal place is 9
  • Deciding digit: The next digit is 9
  • Since 9 ≥ 5, we round up
  • When we round 9 up, it becomes 10, so we carry 1 to the previous digit
  • Answer: 64.840 (3 d.p.)

Notice that we keep the zero at the end to show we've rounded to exactly 3 decimal places.

Example 3: Round 0.295631 to 2 decimal places

  • Target digit: The second decimal place is 9
  • Deciding digit: The next digit is 5
  • Since 5 ≥ 5, we round up
  • The 9 becomes 10, so we carry 1 to the previous digit
  • Answer: 0.30 (2 d.p.)

The zero is important here—it shows we've given the answer to 2 decimal places, not just 1.

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