Converting Decimals to Fractions
Every decimal number can be written as a fraction. For example, 0.5 is the same as 1/2, and 0.75 is the same as 3/4.
Converting a decimal to a fraction is useful when you need to add, subtract, or compare numbers in fraction form.
The method is simple — count the decimal places and use powers of 10 as the denominator.
What is Converting Decimals to Fractions - Grade 6 Maths (Decimals)?
Definition: To convert a decimal to a fraction, write the digits after the decimal point as the numerator and the appropriate power of 10 as the denominator.
Rule:
- 1 decimal place → denominator is 10
- 2 decimal places → denominator is 100
- 3 decimal places → denominator is 1000
Then simplify the fraction to its lowest terms by dividing numerator and denominator by their HCF.
Converting Decimals to Fractions Formula
Steps to convert a decimal to a fraction:
- Write the decimal without the decimal point as the numerator.
- Write 1 followed by as many zeros as there are decimal places as the denominator.
- Simplify the fraction by dividing by the HCF.
Example: 0.25
- Numerator = 25
- 2 decimal places → Denominator = 100
- Fraction = 25/100
- HCF of 25 and 100 = 25
- Simplified = 25 ÷ 25 / 100 ÷ 25 = 1/4
For decimals with a whole number part:
- Convert to a mixed number OR convert the whole decimal directly.
- Example: 2.5 = 25/10 = 5/2 = 2½
Types and Properties
Types of decimals and their fraction forms:
- Terminating decimals: Have a finite number of digits after the decimal point. These always convert to exact fractions. Example: 0.375 = 3/8.
- Decimals with whole parts: Like 3.4 — convert to mixed number (3⅖) or improper fraction (17/5).
Common decimal-to-fraction conversions:
- 0.1 = 1/10
- 0.2 = 1/5
- 0.25 = 1/4
- 0.5 = 1/2
- 0.75 = 3/4
- 0.125 = 1/8
- 0.333... = 1/3 (approximately)
Solved Examples
Example 1: One Decimal Place
Problem: Convert 0.6 to a fraction.
Solution:
- 1 decimal place → denominator = 10
- Fraction = 6/10
- HCF of 6 and 10 = 2
- 6 ÷ 2 / 10 ÷ 2 = 3/5
Answer: 0.6 = 3/5
Example 2: Two Decimal Places
Problem: Convert 0.45 to a fraction.
Solution:
- 2 decimal places → denominator = 100
- Fraction = 45/100
- HCF of 45 and 100 = 5
- 45 ÷ 5 / 100 ÷ 5 = 9/20
Answer: 0.45 = 9/20
Example 3: Three Decimal Places
Problem: Convert 0.125 to a fraction.
Solution:
- 3 decimal places → denominator = 1000
- Fraction = 125/1000
- HCF of 125 and 1000 = 125
- 125 ÷ 125 / 1000 ÷ 125 = 1/8
Answer: 0.125 = 1/8
Example 4: Decimal with Whole Number
Problem: Convert 3.4 to a fraction.
Solution:
- Write as 34/10
- HCF of 34 and 10 = 2
- 34 ÷ 2 / 10 ÷ 2 = 17/5
- As a mixed number: 3 2/5
Answer: 3.4 = 17/5 or 3 2/5
Example 5: Already in Simplest Form
Problem: Convert 0.7 to a fraction.
Solution:
- 1 decimal place → 7/10
- HCF of 7 and 10 = 1 (no common factor)
Answer: 0.7 = 7/10 (already in simplest form)
Example 6: Converting 0.05
Problem: Convert 0.05 to a fraction.
Solution:
- 2 decimal places → denominator = 100
- Fraction = 5/100
- HCF of 5 and 100 = 5
- 5 ÷ 5 / 100 ÷ 5 = 1/20
Answer: 0.05 = 1/20
Example 7: Converting 2.75
Problem: Convert 2.75 to a fraction.
Solution:
- Write as 275/100
- HCF of 275 and 100 = 25
- 275 ÷ 25 / 100 ÷ 25 = 11/4
- As a mixed number: 2 3/4
Answer: 2.75 = 11/4 or 2 3/4
Example 8: Converting 0.008
Problem: Convert 0.008 to a fraction.
Solution:
- 3 decimal places → denominator = 1000
- Fraction = 8/1000
- HCF of 8 and 1000 = 8
- 8 ÷ 8 / 1000 ÷ 8 = 1/125
Answer: 0.008 = 1/125
Real-World Applications
Where decimal-to-fraction conversion is useful:
- Cooking: A recipe says 0.25 kg of sugar — that is 1/4 kg, or 250 grams.
- Measurement: 0.5 metre = 1/2 metre, which is easier to visualise.
- Money: Rs 0.50 = Rs 1/2 = 50 paise.
- Tests and exams: When answers need to be in fraction form.
- Comparing: Sometimes fractions are easier to compare than decimals.
Key Points to Remember
- To convert a decimal to a fraction: digits become the numerator, power of 10 becomes the denominator.
- 1 decimal place → divide by 10; 2 places → 100; 3 places → 1000.
- Always simplify the fraction by dividing numerator and denominator by their HCF.
- Decimals with whole parts can be written as improper fractions or mixed numbers.
- 0.5 = 1/2, 0.25 = 1/4, 0.75 = 3/4, 0.125 = 1/8 — memorise these common conversions.
- If the HCF is 1, the fraction is already in simplest form.
Practice Problems
- Convert 0.8 to a fraction in simplest form.
- Convert 0.36 to a fraction in simplest form.
- Convert 0.625 to a fraction.
- Convert 4.5 to a mixed number.
- Convert 0.02 to a fraction.
- Which is greater: 0.4 or 3/8? (Convert and compare.)
Frequently Asked Questions
Q1. How do I convert a decimal to a fraction?
Count the decimal places. Write the number without the decimal point as the numerator. Write 1 followed by that many zeros as the denominator. Then simplify.
Q2. Why do we use 10, 100, or 1000 as the denominator?
Each decimal place represents a power of 10. The first decimal place is tenths (1/10), the second is hundredths (1/100), and the third is thousandths (1/1000).
Q3. Do I always need to simplify?
Yes. The fraction should be written in its simplest (lowest) form. Divide the numerator and denominator by their HCF.
Q4. What about decimals like 0.333...?
Repeating decimals like 0.333... are equal to 1/3, but converting them is harder and is covered in higher classes. In Class 6, you will mainly work with terminating decimals.
Q5. Can I convert any decimal to a fraction?
Yes. Every terminating decimal (like 0.25, 0.8, 0.125) can be written as an exact fraction. Repeating decimals also have fraction forms.
Q6. How do I handle 0.05 or 0.002 (zeros after the decimal point)?
Count all decimal places including the zeros. 0.05 has 2 decimal places → 5/100 = 1/20. 0.002 has 3 decimal places → 2/1000 = 1/500.
