Number System - Rounding and estimation

Grade 6IGCSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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Rounding to the nearest whole number/10/100: Identifying the target place value and looking at the digit to its immediate right.

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Decimal Places (d.p.): Rounding a number based on the number of digits following the decimal point.

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Significant Figures (s.f.): Identifying the first non-zero digit as the first significant figure and rounding from there.

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The 5+ Rule: If the digit to the right of the target place is 5, 6, 7, 8, or 9, round the target digit up. If it is 4 or less, keep the target digit the same.

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Estimation: Simplifing complex calculations by rounding each number (usually to 1 significant figure) to get a 'rough' answer quickly.

📐Formulae

\text{Error Interval: } L \le x < U \text{ (where } L \text{ is lower bound and } U \text{ is upper bound)}

\text{Rounding Rule: } \text{If digit } \ge 5 \rightarrow \text{round up; If digit } < 5 \rightarrow \text{stay}

\text{Estimation: } \text{Value} \approx \text{Rounded Values Calculation}

💡Examples

Problem 1:

Round 5.672 to 2 decimal places.

Solution:

5.67

Explanation:

Identify the 2nd decimal place (7). Look at the digit to the right (2). Since 2 is less than 5, the digit 7 remains unchanged and the 2 is dropped.

Problem 2:

Round 0.004839 to 2 significant figures.

Solution:

0.0048

Explanation:

The first significant figure is the first non-zero digit (4). The second is 8. The digit following 8 is 3. Since 3 is less than 5, we keep the 8 and drop the remaining digits.

Problem 3:

\frac{59.2 \times 4.1}{0.19}

Solution:

1200

Explanation:

59.2 \approx 60