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Number System - Place value and ordering numbers

Grade 6IGCSE

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

🔑Concepts

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

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Decimal System: The position of a digit relative to the decimal point determines its value (e.g., tenths, hundredths, thousandths).

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Comparing Numbers: Using symbols like >> (greater than), << (less than), and == (equal to) to compare numerical values.

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Ordering: Arranging numbers in Ascending order (smallest to largest) or Descending order (largest to smallest).

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Placeholder Zeros: Using zeros to fill empty places when comparing decimals to ensure they have the same number of decimal places.

📐Formulae

Value of a digit = Digit×Place Value\text{Digit} \times \text{Place Value}

Multiplying by 10n10^n: Move the decimal point nn places to the right.

Dividing by 10n10^n: Move the decimal point nn places to the left.

💡Examples

Problem 1:

In the number 5,820.3475,820.347, what is the place value and the actual value of the digit 44?

Solution:

Place Value: Hundredths; Actual Value: 0.040.04 (or 4100\frac{4}{100})

Explanation:

The first digit after the decimal is tenths, the second is hundredths. Since 4 is in the second position after the decimal, its value is 4 hundredths.

Problem 2:

Arrange the following numbers in ascending order: 0.6,0.066,0.606,0.060.6, 0.066, 0.606, 0.06.

Solution:

0.06,0.066,0.6,0.6060.06, 0.066, 0.6, 0.606

Explanation:

To compare easily, add placeholder zeros so all numbers have three decimal places: 0.600,0.066,0.606,0.0600.600, 0.066, 0.606, 0.060. Comparing these, 60<66<600<60660 < 66 < 600 < 606.

Problem 3:

Insert the correct symbol (<,>,=<, >, =) between the numbers: 4.054.05 ___ 4.0504.050.

Solution:

4.05=4.0504.05 = 4.050

Explanation:

Trailing zeros after the last non-zero digit in a decimal do not change the value of the number.

Problem 4:

Calculate 45.2÷10045.2 \div 100.

Solution:

0.4520.452

Explanation:

When dividing by 100 (which has two zeros), move the decimal point two places to the left.