Converting Decimals to Fractions
Converting decimals to fractions means writing a decimal number as a fraction. For example, 0.5 = 1/2 and 0.75 = 3/4.
This is the reverse of converting fractions to decimals. Both skills together help you move freely between two ways of expressing parts of a whole number. In some situations, fractions are easier to work with (like multiplying 1/4 of something), while in others, decimals are more convenient (like adding money amounts).
In everyday life, you might see a price tag showing ₹12.50 and need to express the paise part (0.50) as a fraction — that is 50/100, which simplifies to 1/2. Or a recipe might say "0.25 kg of sugar" and you need to know that is the same as 1/4 kg.
In this topic, you will learn a simple three-step method to convert any decimal to a fraction, and then how to simplify the fraction to its lowest terms using the HCF.
What is Converting Decimals to Fractions - Class 5 Maths (Decimals)?
A decimal uses the decimal point and place values (tenths, hundredths, thousandths) to show parts of a whole. A fraction uses a numerator (top number) and denominator (bottom number) to show a part of a whole.
Converting a decimal to a fraction means rewriting the decimal as a fraction in the form numerator/denominator, and then simplifying to lowest terms.
The method relies on understanding decimal place values:
| Decimal Places | Place Value Name | Denominator | Example |
|---|---|---|---|
| 1 place | Tenths | 10 | 0.3 = 3/10 |
| 2 places | Hundredths | 100 | 0.47 = 47/100 |
| 3 places | Thousandths | 1000 | 0.125 = 125/1000 |
Converting Decimals to Fractions Formula
Decimal to Fraction: Write the decimal over 10, 100, or 1000 (based on decimal places), then simplify using HCF.
Three-step method:
- Count the decimal places.
- One decimal place → denominator is 10
- Two decimal places → denominator is 100
- Three decimal places → denominator is 1000
- Write the number without the decimal point as the numerator.
- 0.6 → numerator is 6, denominator is 10 → 6/10
- 0.25 → numerator is 25, denominator is 100 → 25/100
- Simplify the fraction by dividing both the numerator and denominator by their HCF (Highest Common Factor).
- 6/10: HCF of 6 and 10 is 2 → 6/10 = 3/5
- 25/100: HCF of 25 and 100 is 25 → 25/100 = 1/4
For decimals greater than 1:
- Separate the whole number part from the decimal part.
- Convert only the decimal part to a fraction.
- Write as a mixed number: whole number + fraction.
Example: 2.75 → whole number = 2, decimal part = 0.75 = 75/100 = 3/4 → answer: 2 3/4
Types and Properties
Type 1: One decimal place (tenths)
The denominator is 10. Simplify if possible.
- 0.3 = 3/10 (already in simplest form — 3 and 10 share no common factor)
- 0.8 = 8/10 = 4/5 (HCF of 8 and 10 is 2)
- 0.5 = 5/10 = 1/2 (HCF of 5 and 10 is 5)
Type 2: Two decimal places (hundredths)
The denominator is 100. Many of these simplify nicely.
- 0.25 = 25/100 = 1/4 (HCF = 25)
- 0.45 = 45/100 = 9/20 (HCF = 5)
- 0.50 = 50/100 = 1/2 (HCF = 50)
- 0.12 = 12/100 = 3/25 (HCF = 4)
Type 3: Three decimal places (thousandths)
The denominator is 1000.
- 0.125 = 125/1000 = 1/8 (HCF = 125)
- 0.375 = 375/1000 = 3/8 (HCF = 125)
- 0.008 = 8/1000 = 1/125 (HCF = 8)
Type 4: Decimals greater than 1 (mixed numbers)
Separate the whole number, convert only the decimal part.
- 2.5 = 2 + 0.5 = 2 + 5/10 = 2 + 1/2 = 2 1/2
- 3.75 = 3 + 0.75 = 3 + 75/100 = 3 + 3/4 = 3 3/4
- 4.2 = 4 + 0.2 = 4 + 2/10 = 4 + 1/5 = 4 1/5
Solved Examples
Example 1: One Decimal Place — No Simplification Needed
Problem: Convert 0.7 to a fraction.
Solution:
Step 1: 0.7 has 1 decimal place, so the denominator = 10.
Step 2: Write without decimal: 7. So the fraction is 7/10.
Step 3: Check for simplification: 7 is a prime number and does not divide 10. So 7/10 is already in simplest form.
Answer: 0.7 = 7/10
Example 2: One Decimal Place — Simplification Required
Problem: Convert 0.4 to a fraction in simplest form.
Solution:
Step 1: 0.4 has 1 decimal place → denominator = 10. Fraction = 4/10.
Step 2: Find HCF of 4 and 10. Factors of 4: 1, 2, 4. Factors of 10: 1, 2, 5, 10. HCF = 2.
Step 3: Divide both by 2: 4 ÷ 2 = 2, 10 ÷ 2 = 5. Simplified: 2/5.
Verification: 2 ÷ 5 = 0.4 ✓
Answer: 0.4 = 2/5
Example 3: Two Decimal Places — 0.75
Problem: Convert 0.75 to a fraction in simplest form.
Solution:
Step 1: 0.75 has 2 decimal places → denominator = 100. Fraction = 75/100.
Step 2: HCF of 75 and 100: Factors of 75: 1, 3, 5, 15, 25, 75. Factors of 100: 1, 2, 4, 5, 10, 20, 25, 50, 100. HCF = 25.
Step 3: 75 ÷ 25 = 3, 100 ÷ 25 = 4.
Verification: 3 ÷ 4 = 0.75 ✓
Answer: 0.75 = 3/4
Example 4: Three Decimal Places — 0.125
Problem: Convert 0.125 to a fraction in simplest form.
Solution:
Step 1: 0.125 has 3 decimal places → denominator = 1000. Fraction = 125/1000.
Step 2: HCF of 125 and 1000 = 125 (since 125 × 8 = 1000).
Step 3: 125 ÷ 125 = 1, 1000 ÷ 125 = 8.
Verification: 1 ÷ 8 = 0.125 ✓
Answer: 0.125 = 1/8
Example 5: Decimal Greater Than 1 — Mixed Number
Problem: Convert 2.6 to a mixed number in simplest form.
Solution:
Step 1: Separate: whole number part = 2, decimal part = 0.6.
Step 2: Convert 0.6: has 1 decimal place → 6/10.
Step 3: Simplify: HCF of 6 and 10 = 2. So 6/10 = 3/5.
Step 4: Combine: 2 + 3/5 = 2 3/5.
Answer: 2.6 = 2 3/5
Example 6: Word Problem — Money
Problem: Ria saved ₹0.50 from her pocket money. Express this amount as a fraction of one rupee.
Solution:
Step 1: 0.50 has 2 decimal places → 50/100.
Step 2: HCF of 50 and 100 = 50.
Step 3: 50 ÷ 50 = 1, 100 ÷ 50 = 2.
Real-life meaning: 50 paise is half a rupee.
Answer: ₹0.50 = 1/2 rupee
Example 7: Word Problem — Measurement
Problem: A pencil is 0.15 m long. Express this length as a fraction of a metre in simplest form.
Solution:
Step 1: 0.15 has 2 decimal places → 15/100.
Step 2: HCF of 15 and 100 = 5.
Step 3: 15 ÷ 5 = 3, 100 ÷ 5 = 20.
Real-life meaning: The pencil is 3/20 of a metre, or 15 cm.
Answer: 0.15 m = 3/20 m
Example 8: Small Decimal — 0.05
Problem: Convert 0.05 to a fraction in simplest form.
Solution:
Step 1: 0.05 has 2 decimal places → 5/100.
Step 2: HCF of 5 and 100 = 5.
Step 3: 5 ÷ 5 = 1, 100 ÷ 5 = 20.
Note: 0.05 is a small number — just 5 hundredths, or 1 part out of 20.
Answer: 0.05 = 1/20
Example 9: Mixed Number — 4.25
Problem: Convert 4.25 to a mixed number in simplest form.
Solution:
Step 1: Whole number part = 4. Decimal part = 0.25.
Step 2: 0.25 has 2 decimal places → 25/100.
Step 3: HCF of 25 and 100 = 25. So 25/100 = 1/4.
Step 4: Combined: 4 + 1/4 = 4 1/4.
Real-life context: If Dev ran 4.25 km, he ran 4 and 1/4 kilometres.
Answer: 4.25 = 4 1/4
Example 10: Common Decimals to Fractions — Reference Table
Problem: Convert each decimal to a fraction in simplest form: 0.1, 0.2, 0.25, 0.5, 0.75, 0.125.
Solution:
| Decimal | As Fraction | HCF | Simplest Form |
|---|---|---|---|
| 0.1 | 1/10 | 1 | 1/10 |
| 0.2 | 2/10 | 2 | 1/5 |
| 0.25 | 25/100 | 25 | 1/4 |
| 0.5 | 5/10 | 5 | 1/2 |
| 0.75 | 75/100 | 25 | 3/4 |
| 0.125 | 125/1000 | 125 | 1/8 |
Tip: Memorise these common conversions — they appear frequently in exams and daily life.
Real-World Applications
Real-life uses of converting decimals to fractions:
- Money: ₹0.25 = 25 paise = 1/4 rupee. Understanding this helps when splitting bills or calculating change.
- Cooking: A recipe calls for 0.5 kg of sugar — that is 1/2 kg. Easier to measure with a kitchen scale marked in fractions.
- Measurement: 0.75 m of ribbon is the same as 3/4 m. When cutting cloth, tailors often think in fractions.
- Sports: If a cricketer's batting average is 0.375, that means they score runs 3 out of every 8 times they face a ball.
- Exams: A score of 0.8 out of 1 = 4/5. Converting helps understand what fraction of marks was scored.
- Science: Concentrations are often expressed as decimals but need to be converted to fractions for ratio calculations.
Key Points to Remember
- To convert a decimal to a fraction: count the decimal places, use the correct denominator (10, 100, or 1000), write the digits as the numerator, and simplify.
- 1 decimal place → denominator 10. 2 decimal places → denominator 100. 3 decimal places → denominator 1000.
- Always simplify the fraction by dividing both numerator and denominator by their HCF.
- For decimals greater than 1, separate the whole number and convert only the decimal part to get a mixed number.
- Trailing zeros after the last non-zero decimal digit can be ignored: 0.50 = 0.5 = 1/2.
- Common conversions to memorise: 0.5 = 1/2, 0.25 = 1/4, 0.75 = 3/4, 0.2 = 1/5, 0.125 = 1/8.
- Verification: after converting, divide the numerator by the denominator — you should get back the original decimal.
Practice Problems
- Convert 0.9 to a fraction in simplest form.
- Convert 0.36 to a fraction in simplest form.
- Express 0.625 as a fraction in simplest form.
- Priya has a rope 0.45 m long. Express this as a fraction of a metre.
- Convert 3.8 to a mixed number in simplest form.
- Write 0.08 as a fraction in simplest form.
- Aman scored 0.65 in a quiz (out of 1). Express his score as a fraction in simplest form.
- Convert 7.125 to a mixed number in simplest form.
Frequently Asked Questions
Q1. How do you convert a decimal to a fraction?
Follow three steps: (1) Count the decimal places to determine the denominator — 1 place means 10, 2 places means 100, 3 places means 1000. (2) Write the digits without the decimal point as the numerator. (3) Simplify by dividing both by their HCF. For example, 0.35 = 35/100 = 7/20.
Q2. What is 0.5 as a fraction?
0.5 has 1 decimal place, so it becomes 5/10. Simplify: HCF of 5 and 10 is 5, so 5/10 = 1/2.
Q3. How do you simplify a fraction after converting from a decimal?
Find the HCF (Highest Common Factor) of the numerator and denominator, then divide both by it. For 75/100: HCF of 75 and 100 is 25, so 75 ÷ 25 = 3 and 100 ÷ 25 = 4, giving 3/4.
Q4. What is 0.333... as a fraction?
0.333... (repeating) equals 1/3. This is a special case — repeating decimals come from fractions whose denominators have prime factors other than 2 and 5. At the Class 5 level, you mainly work with terminating decimals.
Q5. How do you convert a decimal greater than 1 to a fraction?
Separate the whole number and the decimal part. Convert only the decimal part to a fraction, then write as a mixed number. For example, 2.75 = 2 + 0.75 = 2 + 75/100 = 2 + 3/4 = 2 3/4.
Q6. Does 0.50 equal 0.5?
Yes. Trailing zeros after the last non-zero decimal digit do not change the value. 0.50 and 0.5 both equal 5/10 = 1/2. You can always remove trailing zeros.
Q7. What is the denominator for 3 decimal places?
The denominator is 1000. For example, 0.375 has 3 decimal places, so it becomes 375/1000, which simplifies to 3/8.
Q8. Why is it useful to convert decimals to fractions?
Fractions are often easier to work with in multiplication, division, and ratio problems. For instance, finding 1/4 of a number (divide by 4) is simpler mental maths than multiplying by 0.25. Fractions also show exact values that decimals sometimes cannot (like 1/3).
Q9. Can all decimals be converted to fractions?
All terminating decimals (like 0.6, 0.25, 0.125) can be exactly converted to fractions. Repeating decimals (like 0.333...) also have exact fraction equivalents (1/3). Only non-repeating, non-terminating decimals (like the value of pi = 3.14159...) cannot be written as exact fractions.
Related Topics
- Converting Fractions to Decimals (Grade 5)
- Decimals (Grade 5)
- Comparing and Ordering Decimals
- Addition of Decimals
- Subtraction of Decimals
- Multiplication of Decimals
- Division of Decimals
- Decimal Word Problems (Grade 5)
- Decimal Place Value (Grade 5)
- Rounding Decimals
- Multiplying Decimals by 10, 100 and 1000
- Dividing Decimals by 10, 100 and 1000
