Converting Fractions to Decimals (Grade 5)
Converting fractions to decimals is an essential skill in Class 5 Maths. A fraction like 3/4 can be written as the decimal 0.75. Both represent the same value — just in different forms.
Decimals are often easier to compare, add, and subtract than fractions, especially when dealing with money and measurements. Knowing how to convert between these two forms makes problem-solving faster and more flexible.
For example, when comparing prices — is 3/4 of a kilogram more or less than 0.7 kg? Converting 3/4 to 0.75 immediately shows it is more than 0.7.
In this topic, you will learn two methods for converting fractions to decimals: the equivalent fraction method and the long division method. You will also learn to convert mixed numbers to decimals.
What is Converting Fractions to Decimals - Class 5 Maths (Decimals)?
A fraction represents a part of a whole using two numbers — the numerator (top) tells how many parts you have, and the denominator (bottom) tells how many equal parts the whole is divided into.
A decimal also represents a part of a whole, but uses a decimal point and place values — tenths (1/10), hundredths (1/100), thousandths (1/1000), and so on.
Converting a fraction to a decimal means expressing the fraction in decimal form.
The fundamental rule is simple: divide the numerator by the denominator.
For example:
- 1/2 = 1 ÷ 2 = 0.5
- 3/4 = 3 ÷ 4 = 0.75
- 1/5 = 1 ÷ 5 = 0.2
Converting Fractions to Decimals (Grade 5) Formula
Fraction to Decimal: Divide the numerator by the denominator
a/b = a ÷ b
Method 1: Long Division
- Divide the numerator by the denominator.
- If the numerator is smaller than the denominator, write 0 and a decimal point, then add zeros to continue dividing.
- Keep dividing until the remainder is 0 (terminating decimal) or you see a repeating pattern.
- The quotient is the decimal form of the fraction.
Method 2: Equivalent Fraction with denominator 10, 100, or 1000
- Check if the denominator can be easily converted to 10, 100, or 1000 by multiplication.
- Multiply both the numerator and denominator by the same number to get 10, 100, or 1000 in the denominator.
- Once the denominator is 10, 100, or 1000, the numerator directly gives the decimal digits.
Which denominators work for Method 2?
- Denominator 2 → multiply by 5 to get 10
- Denominator 4 → multiply by 25 to get 100
- Denominator 5 → multiply by 2 to get 10
- Denominator 8 → multiply by 125 to get 1000
- Denominator 20 → multiply by 5 to get 100
- Denominator 25 → multiply by 4 to get 100
- Denominator 50 → multiply by 2 to get 100
For denominators like 3, 6, 7, 9, 11, etc., use the long division method.
Types and Properties
Type 1: Fractions with denominator 10, 100, or 1000
These are the easiest to convert. Simply place the numerator in the correct decimal place.
- 7/10 = 0.7 (one decimal place)
- 23/100 = 0.23 (two decimal places)
- 9/1000 = 0.009 (three decimal places)
- 156/100 = 1.56 (greater than 1)
Type 2: Fractions whose denominator can be made 10 or 100
Find a number to multiply the denominator by to reach 10 or 100, and multiply the numerator by the same number.
- 1/2 = (1 × 5)/(2 × 5) = 5/10 = 0.5
- 3/4 = (3 × 25)/(4 × 25) = 75/100 = 0.75
- 7/20 = (7 × 5)/(20 × 5) = 35/100 = 0.35
- 3/50 = (3 × 2)/(50 × 2) = 6/100 = 0.06
Type 3: Fractions requiring long division
When the denominator cannot easily become 10 or 100, use division.
- 1/3 = 1 ÷ 3 = 0.333... (repeating decimal)
- 5/6 = 5 ÷ 6 = 0.833...
- 2/7 = 2 ÷ 7 = 0.2857...
Type 4: Mixed numbers to decimals
Keep the whole number part. Convert only the fraction part to a decimal and add.
- 2 3/4 = 2 + 0.75 = 2.75
- 5 1/2 = 5 + 0.5 = 5.5
- 1 3/8 = 1 + 0.375 = 1.375
Solved Examples
Example 1: Fraction with Denominator 10
Problem: Convert 3/10 to a decimal.
Solution:
Step 1: The denominator is already 10.
Step 2: For denominator 10, place the numerator in the tenths place (one digit after decimal).
Step 3: 3/10 = 0.3
Answer: 3/10 = 0.3
Example 2: Fraction with Denominator 100
Problem: Convert 47/100 to a decimal.
Solution:
Step 1: The denominator is already 100.
Step 2: For denominator 100, the numerator occupies the tenths and hundredths places (two digits after decimal).
Step 3: 47/100 = 0.47
Note: If the numerator has fewer digits than needed, add a leading zero. For example, 7/100 = 0.07 (not 0.7).
Answer: 47/100 = 0.47
Example 3: Making the Denominator 10
Problem: Convert 2/5 to a decimal.
Solution:
Step 1: Can we make the denominator 10? Yes: 5 × 2 = 10.
Step 2: Multiply both numerator and denominator by 2:
2/5 = (2 × 2)/(5 × 2) = 4/10
Step 3: 4/10 = 0.4
Verification: 2 ÷ 5 = 0.4 ✓
Answer: 2/5 = 0.4
Example 4: Making the Denominator 100
Problem: Convert 3/4 to a decimal.
Solution:
Step 1: Can we make the denominator 10? 4 × 2.5 = 10 — not a whole number, so try 100.
Step 2: 4 × 25 = 100. Multiply numerator and denominator by 25.
Step 3: 3/4 = (3 × 25)/(4 × 25) = 75/100
Step 4: 75/100 = 0.75
Verification: 3 ÷ 4 = 0.75 ✓
Answer: 3/4 = 0.75
Example 5: Using Long Division — 5/8
Problem: Convert 5/8 to a decimal.
Solution:
Step 1: Divide 5 by 8. Since 5 is less than 8, write 0. and add zeros to continue.
Step 2: 50 ÷ 8 = 6, remainder 2. Quotient so far: 0.6
Step 3: 20 ÷ 8 = 2, remainder 4. Quotient: 0.62
Step 4: 40 ÷ 8 = 5, remainder 0. Quotient: 0.625
Step 5: Remainder is 0, so division is complete.
Verification: 0.625 × 8 = 5 ✓
Answer: 5/8 = 0.625
Example 6: Converting a Mixed Number — 3 1/4
Problem: Convert 3 1/4 to a decimal.
Solution:
Step 1: Separate the whole number: 3
Step 2: Convert the fraction part: 1/4 = (1 × 25)/(4 × 25) = 25/100 = 0.25
Step 3: Add the whole number and decimal: 3 + 0.25 = 3.25
Answer: 3 1/4 = 3.25
Example 7: Word Problem — Pizza Sharing
Problem: Aditi ate 3/8 of a pizza. Express the amount she ate as a decimal.
Solution:
Step 1: We need to convert 3/8 to a decimal. Use long division: 3 ÷ 8.
Step 2: 30 ÷ 8 = 3, remainder 6. Quotient: 0.3
Step 3: 60 ÷ 8 = 7, remainder 4. Quotient: 0.37
Step 4: 40 ÷ 8 = 5, remainder 0. Quotient: 0.375
Answer: Aditi ate 0.375 of the pizza.
Example 8: Word Problem — Fabric Length
Problem: Meera needs 7/20 metres of fabric for a craft project. Express this length as a decimal.
Solution:
Step 1: Can we make the denominator 100? Yes: 20 × 5 = 100.
Step 2: Multiply numerator and denominator by 5:
7/20 = (7 × 5)/(20 × 5) = 35/100
Step 3: 35/100 = 0.35
Answer: Meera needs 0.35 m of fabric.
Example 9: Fraction with Denominator 25
Problem: Convert 9/25 to a decimal.
Solution:
Step 1: 25 × 4 = 100. Multiply both by 4.
Step 2: 9/25 = (9 × 4)/(25 × 4) = 36/100
Step 3: 36/100 = 0.36
Verification: 9 ÷ 25 = 0.36 ✓
Answer: 9/25 = 0.36
Example 10: Common Fractions Reference Table
Problem: Complete the table showing the decimal form for common fractions.
Solution:
| Fraction | Method Used | Decimal |
|---|---|---|
| 1/2 | 1/2 = 5/10 | 0.5 |
| 1/4 | 1/4 = 25/100 | 0.25 |
| 3/4 | 3/4 = 75/100 | 0.75 |
| 1/5 | 1/5 = 2/10 | 0.2 |
| 3/5 | 3/5 = 6/10 | 0.6 |
| 1/8 | Long division | 0.125 |
| 3/8 | Long division | 0.375 |
| 1/10 | Already /10 | 0.1 |
Tip: Memorise these common conversions to save time during exams and calculations.
Real-World Applications
Where is fraction-to-decimal conversion used in real life?
- Money: Half a rupee = ₹0.50 (1/2 = 0.5). Quarter of a rupee = ₹0.25 (1/4 = 0.25). Shopkeepers and banks always use decimals for money.
- Measurement: A quarter of a metre = 0.25 m. Construction workers, tailors, and carpenters use decimal measurements.
- Comparing values: It is easier to compare 0.75 and 0.6 than to compare 3/4 and 3/5. Decimals line up by place value for quick comparison.
- Calculators: Calculators display results in decimals, so knowing the conversion helps verify your answers against the calculator.
- Scoring and rankings: If Arjun scored 18 out of 25 in a quiz, his score is 18/25 = 0.72 (or 72%). Rankings are often based on decimal scores.
- Science experiments: Data from experiments is recorded in decimals — knowing how to convert fractions helps in data analysis.
Key Points to Remember
- To convert a fraction to a decimal, divide the numerator by the denominator.
- If the denominator is already 10, 100, or 1000, directly place the numerator with the correct number of decimal places.
- If the denominator is 2, 4, 5, 20, 25, or 50, find an equivalent fraction with denominator 10 or 100.
- For denominators like 3, 6, 7, 8, or 9, use long division.
- Some fractions give terminating decimals (e.g., 1/4 = 0.25 — the digits end).
- Some fractions give repeating decimals (e.g., 1/3 = 0.333... — the digits repeat forever).
- For mixed numbers, convert only the fraction part and add it to the whole number.
- Memorising common conversions (1/2 = 0.5, 1/4 = 0.25, 3/4 = 0.75, 1/5 = 0.2, 1/8 = 0.125) speeds up calculations.
- Always verify: multiply the decimal by the denominator — you should get the numerator.
Practice Problems
- Convert 7/10 to a decimal.
- Convert 4/5 to a decimal using the equivalent fraction method.
- Express 3/8 as a decimal using long division.
- Ria drank 1/4 of a litre of juice. Express this in decimal form.
- Convert 63/100 to a decimal.
- Write 5 3/20 as a decimal.
- Dev scored 17/25 in a test. What is his score as a decimal?
- Convert 11/40 to a decimal.
Frequently Asked Questions
Q1. How do you convert a fraction to a decimal?
Divide the numerator by the denominator. For example, 3/4 = 3 ÷ 4 = 0.75. Alternatively, if the denominator can be made 10 or 100, use the equivalent fraction method: 3/4 = 75/100 = 0.75.
Q2. What is 1/3 as a decimal?
1/3 = 1 ÷ 3 = 0.333... (the 3 repeats forever). This is called a repeating or recurring decimal. In Class 5, you may write it as approximately 0.33.
Q3. Can every fraction be converted to a decimal?
Yes, every fraction can be written as a decimal. Some give terminating decimals (like 1/4 = 0.25) and some give repeating decimals (like 1/3 = 0.333...). Both are valid decimal representations.
Q4. What is the easiest method to convert a fraction to a decimal?
If the denominator can be made 10 or 100 easily, use the equivalent fraction method — it avoids long division entirely. For example, 3/5 = 6/10 = 0.6 requires no division. For other fractions, long division is the reliable method.
Q5. How do you convert a mixed number to a decimal?
Keep the whole number part as it is and convert only the fraction part to a decimal, then add them together. For example, 4 1/2 = 4 + 0.5 = 4.5.
Q6. What are terminating and non-terminating decimals?
A terminating decimal has a fixed number of decimal digits and then stops (e.g., 0.25, 0.6, 0.125). A non-terminating decimal goes on forever (e.g., 0.333..., 0.1666...). Fractions whose denominators (in simplest form) have only 2 and 5 as prime factors always give terminating decimals.
Q7. Which common fractions should I memorise as decimals?
The most useful ones are: 1/2 = 0.5, 1/4 = 0.25, 3/4 = 0.75, 1/5 = 0.2, 2/5 = 0.4, 3/5 = 0.6, 4/5 = 0.8, 1/8 = 0.125, 1/10 = 0.1, and 1/3 ≈ 0.33.
Q8. Why is converting fractions to decimals useful?
Decimals are easier to compare (0.75 vs 0.6 is quicker than comparing 3/4 and 3/5). They are also used universally in money, measurements, science, and technology. Calculators and computers work with decimals.
Q9. Is 0.5 the same as 1/2?
Yes, 0.5 and 1/2 represent exactly the same value. They are just two different ways of writing the same number. You can verify: 1 ÷ 2 = 0.5, and 0.5 × 2 = 1.
Related Topics
- Converting Decimals to Fractions
- Converting Fractions to Decimals (Grade 4)
- 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
