Number - Place value, ordering and rounding

Grade 7IGCSE

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

🔑Concepts

•

Place Value Chart: Understanding the position of digits from Millions down to Thousandths.

•

Decimals: Comparing and ordering decimals by aligning the decimal points and comparing digits from left to right.

•

Multiplying and Dividing by Powers of 10: Shifting the decimal point to the right (multiplication) or left (division).

•

Rounding to Decimal Places (d.p.): Identifying the target digit and looking at the next digit to decide whether to round up or stay the same.

•

Significant Figures (s.f.): Identifying the first non-zero digit as the first significant figure and rounding based on precision requirements.

•

Estimation: Rounding numbers to 1 significant figure before performing calculations to find an approximate answer.

📐Formulae

\text{Value of digit} = \text{digit} \times \text{place value}

x \times 10^n \rightarrow \text{Move decimal } n \text{ places right}

x \div 10^n \rightarrow \text{Move decimal } n \text{ places left}

\text{If next digit} \geq 5 \rightarrow \text{Round up}

\text{If next digit} < 5 \rightarrow \text{Keep the digit}

💡Examples

Problem 1:

Arrange the following numbers in ascending order: 0.45, 0.405, 0.045, 0.5.

Solution:

0.045, 0.405, 0.45, 0.5

Explanation:

To compare, equalize the number of decimal places: 0.450, 0.405, 0.045, 0.500. Comparing these values, 0.045 is the smallest and 0.500 is the largest.

Problem 2:

Round 12.3456 to 2 decimal places.

Solution:

12.35

Explanation:

The 2nd decimal place is 4. The digit following it is 5. Since it is 5 or greater, we round the 4 up to 5.

Problem 3:

Round 0.007082 to 2 significant figures.

Solution:

0.0071

Explanation:

The first significant figure is 7 (the first non-zero digit). The second is 0. The digit after 0 is 8, so we round the 0 up to 1.

Problem 4:

\frac{4.9 imes 21.2}{0.48}

Solution:

200

Explanation:

4.9 \approx 5