Grades Grade 7 The Number SystemFractions, Decimals & Repeating Patterns

Fractions, Decimals & Repeating Patterns

🔢 The Number System

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Fractions, Decimals & Repeating Patterns

Every rational number can be written as a fraction or a decimal — convert between them fluently.

A rational number can always be expressed as a fraction p/q where p and q are integers and q ≠ 0. When you divide p by q, the decimal either terminates (ends) or repeats in a pattern.

\frac{1}{4} = 0.25 \quad \frac{1}{3} = 0.\overline{3} \quad \frac{5}{6} = 0.8\overline{3}

🔁Converting a repeating decimal to a fraction

Let x = 0.̄7 (0.777…)
Then 10x = 7.777…
10x − x = 7.777… − 0.777…
9x = 7 → x = 7/9

x = 0.\overline{7} \Rightarrow 10x - x = 7 \Rightarrow 9x = 7 \Rightarrow x = \frac{7}{9}

Fraction → Decimal:

1Divide the numerator by the denominator using long division

2If the remainder becomes 0, the decimal terminates

3If the remainder repeats, the decimal repeats — write with a bar over the repeating digits

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Remember This!

Memorize common conversions: 1/2 = 0.5, 1/4 = 0.25, 3/4 = 0.75, 1/3 = 0.333…, 2/3 = 0.666…, 1/8 = 0.125.

✏️ Try It!

Which decimal is equivalent to 5/8?

Practice with CalcVerse

🔄Fraction ↔ Decimal ↔ %✂️Fraction Simplifier

Take Quiz 📝 — 25 Questions