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Fractions, Decimals, and Percentages - Relating fractions to decimals and percentages

Grade 4IGCSE

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

🔑Concepts

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Equivalence: Fractions, decimals, and percentages are different ways of showing the same value or part of a whole.

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Decimals and Tenths: A decimal with one digit after the point represents tenths (e.g., 0.1=1100.1 = \frac{1}{10}).

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Decimals and Hundredths: A decimal with two digits after the point represents hundredths (e.g., 0.01=11000.01 = \frac{1}{100}).

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Percentage Meaning: The word 'percent' means 'out of 100'. The symbol used is '%'.

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The 100-Grid Model: A 10×1010 \times 10 grid is often used to visualize these relationships, where 1 small square equals 1%1\%, 0.010.01, or 1100\frac{1}{100}.

📐Formulae

Percentage=Numerator100×100%\text{Percentage} = \frac{\text{Numerator}}{100} \times 100\%

Fraction to Decimal (for tenths):a10=0.a\text{Fraction to Decimal (for tenths)}: \frac{a}{10} = 0.a

Fraction to Decimal (for hundredths):ab100=0.ab\text{Fraction to Decimal (for hundredths)}: \frac{ab}{100} = 0.ab

Decimal to Percentage:Decimal×100\text{Decimal to Percentage}: \text{Decimal} \times 100

💡Examples

Problem 1:

Convert the fraction 34\frac{3}{4} into a percentage and a decimal.

Solution:

Decimal: 0.750.75, Percentage: 75%75\%

Explanation:

To convert 34\frac{3}{4}, we first make the denominator 100. 3×254×25=75100\frac{3 \times 25}{4 \times 25} = \frac{75}{100}. As a decimal, 75100\frac{75}{100} is 0.750.75. As a percentage, it is 7575 out of 100100, which is 75%75\%.

Problem 2:

A grid has 100 squares. 40 squares are colored red. Write this as a fraction (in simplest form), a decimal, and a percentage.

Solution:

Fraction: 25\frac{2}{5}, Decimal: 0.40.4, Percentage: 40%40\%

Explanation:

40 out of 100 squares is 40100\frac{40}{100}. Simplified, 40100=410=25\frac{40}{100} = \frac{4}{10} = \frac{2}{5}. In decimal form, 40100\frac{40}{100} is 0.400.40 or 0.40.4. As a percentage, it is simply 40%40\%.

Problem 3:

Express 0.070.07 as a fraction and a percentage.

Solution:

Fraction: 7100\frac{7}{100}, Percentage: 7%7\%

Explanation:

The digit 7 is in the hundredths place, so the fraction is 7100\frac{7}{100}. Since percentage is 'out of 100', 7100\frac{7}{100} is equal to 7%7\%.