Fraction ↔ Decimal

1Summary 重點摘要

12 = 0.5; 0.25 = 14.

2Vocabulary cards Vocabulary

3Step by step Steps

1. Part 1: Fractions with denominator 10A fraction with denominator 10 can be written as a one-place decimal: 310 has denominator 10, meaning 3 parts taken out of 10, written as the decimal 0.3 with one place after the dot; likewise 710 = 0.7 and 910 = 0.9. Why can it be written directly? Because the first place after the decimal point is called the tenths place, exactly meaning tenths, matching denominator 10 perfectly. For example, 310 of a dollar is 0.3 dollars, that is 30 cents; both writings name the same amount. Remember the place order: the first place to the right of the ones place is the tenths place. A common mistake is to write 310 as 0.03, adding an extra zero; after writing, count the places after the dot — denominator 10 must give exactly one place.
2. Part 2: Fractions with denominator 100A fraction with denominator 100 can be written as a two-place decimal: 45100 = 0.45, two places after the dot. Filling zeros needs special care: 9100 = 0.09 — a 0 must fill the place before the 9, or it would wrongly become 0.9; likewise 27100 = 0.27 and 5100 = 0.05. Why fill zeros? Because the first decimal place is tenths and only the second is hundredths; a fraction over 100 occupies the hundredths place, so an empty tenths place must hold a 0 to keep the places lined up and the value unchanged. For example, 5100 of a dollar is 0.05 dollars, that is 5 cents; writing 0.5 dollars would mean 50 cents, ten times too much. A common mistake is to write 9100 as 0.9; after writing, check the places — denominator 100 must give two places, filling gaps with 0.
3. Part 3: Simplify after convertingTo change a decimal into a fraction, first write it over 10 or 100 according to the number of places, then simplify to the simplest form. For example, 0.5 first becomes 510, divide top and bottom by 5, and it simplifies to 12; 0.25 = 25100, divided by 25, simplifies to 14; 0.75 = 75100 = 34. Why simplify? Because mathematics prefers fractions in simplest form — writing 12 is more standard than 510 — and a simplified fraction shows its relation to other fractions more clearly: knowing 0.25 = 14 makes comparing 14 with 12 easy. The quickest simplification finds the greatest common factor of the top and the bottom; for 25 and 100 it is 25, finishing in one step. A common mistake is to skip simplifying and stop at 510 for 0.5, or to stop halfway, turning 25100 into 520 when it still simplifies to 14.
4. Part 4: The division routeAny fraction can become a decimal by division: divide the numerator by the denominator, and the quotient is the decimal. For example, 12 = 1 ÷ 2 = 0.5; 14 = 1 ÷ 4 = 0.25; 15 = 1 ÷ 5 = 0.2; 34 = 3 ÷ 4 = 0.75. Why does division work? Because a fraction means equal sharing to begin with: 34 is the result of sharing 3 among 4, exactly 3 divided by 4. The method applies to every fraction, even when the denominator is not 10 or 100: 18 = 1 ÷ 8 = 0.125. A common mistake is to swap the numerator and the denominator, computing 4 ÷ 1 for 14 and getting 4; remember 'numerator on top, divided first' — the numerator is the dividend and the denominator the divisor. Cases that never divide exactly are rare at primary level; when they occur, round as the question requires.
5. Part 5: Learn the common pairsThese fraction-decimal pairs should be memorised: 12 = 0.5, 14 = 0.25, 34 = 0.75, 15 = 0.2, 25 = 0.4, 110 = 0.1, 120 = 0.05. Why memorise them? Because they appear again and again in tests and in life — discounts, measuring lengths, timing — and knowing them lets you write answers straight away, saves calculation time, and supports estimation checks: having found 78 = 0.875, since 78 is just below 1, the answer looks right. Memorise in chains: fix 14 = 0.25 first and derive 34 = 0.75; fix 15 = 0.2 and derive 25 = 0.4, 35 = 0.6, 45 = 0.8, one pair leading to a family. A common mistake is to remember 15 as 0.5, mixing it with 12; after memorising, review each pair once by dividing the numerator by the denominator.
6. Part 6: Conversions in daily lifeFractions and decimals work interchangeably in life: 0.5 dollars is 12 of a dollar, that is 50 cents; 0.75 of a bottle left means 34 left; finishing 0.9 of the homework means 910 is done; a measured length of 1.2 metres is 1 and 15 metres. Why convert at all? Because questions and daily information use fractions sometimes and decimals other times, and only after converting can we compare sizes or add and subtract. For example, comparing 0.6 with 35: turning 35 into 0.6 shows they are equal; comparing 0.7 with 34: turning 34 into 0.75 shows 0.7 is smaller. Unifying the form is the fixed first step of such questions. A common mistake is to compare the bare numbers across different forms with no reason given; convert to one form first, then compare place by place as decimals or compare by common denominators as fractions.

4Diagrams Diagrams

5Worked example Example

6Common mistakes Mistakes

7Quick check Quick check

8Recap Recap

• One decimal place → over 10; two places → over 100
• 0.5 = 12; 0.25 = 14; 0.75 = 34
• Simplify fractions after converting
• Fraction to decimal: numerator ÷ denominator
• Fractions, decimals and percentages are one amount in different forms