Converting Fractions to Decimals
You already know fractions like 1/2 and 3/4, and you know decimals like 0.5 and 0.75. But did you notice that 1/2 and 0.5 mean the same thing? Every fraction can be written as a decimal.
Converting fractions to decimals is very useful. Decimals are easier to compare, add, and use in calculations. When you go shopping, prices are in decimals (Rs 25.50), not fractions (Rs 25 and 1/2).
There are two simple methods to convert a fraction to a decimal: the division method and the equivalent fraction method. We will learn both.
What is Converting Fractions to Decimals - Grade 6 Maths (Decimals)?
Definition: Converting a fraction to a decimal means writing the fraction in decimal form (using a decimal point).
Key idea: A fraction a/b means a ÷ b. So to convert any fraction to a decimal, simply divide the numerator by the denominator.
Types of decimal results:
- Terminating decimal — the division ends after a few steps. Example: 1/4 = 0.25 (the division stops).
- Non-terminating repeating decimal — the division never ends, but digits repeat in a pattern. Example: 1/3 = 0.333... (the 3 keeps repeating).
For Class 6, we mainly work with fractions that give terminating decimals.
Converting Fractions to Decimals Formula
Method 1: Division Method
Fraction a/b = a ÷ b
Simply divide the numerator by the denominator using long division.
Method 2: Equivalent Fraction Method
Make the denominator 10, 100, or 1000, then write as a decimal.
Steps for Method 2:
- Check if the denominator can be converted to 10, 100, or 1000 by multiplying.
- Multiply both numerator and denominator by the same number.
- Write the result as a decimal using place value.
Derivation and Proof
Let us convert 3/4 to a decimal using both methods:
Method 1: Division
- Divide 3 by 4.
- 4 does not go into 3, so write 0 and add a decimal point.
- 30 ÷ 4 = 7, remainder 2. Write 7 after the decimal.
- 20 ÷ 4 = 5, remainder 0. Write 5.
- Division ends. 3 ÷ 4 = 0.75.
Method 2: Equivalent Fraction
- The denominator is 4. We need to make it 100.
- 4 × 25 = 100. So multiply both by 25.
- 3 × 25 = 75, 4 × 25 = 100.
- 3/4 = 75/100 = 0.75.
Both methods give the same answer: 3/4 = 0.75.
Types and Properties
Types of conversion problems:
- Type 1: Simple fractions with denominator 2, 4, 5, 8, 10, 20, 25, 50 — These give neat terminating decimals. Use the equivalent fraction method (make denominator 10 or 100).
- Type 2: Fractions needing long division — When the denominator cannot easily be made 10 or 100. Use division. Example: 5/8.
- Type 3: Mixed numbers to decimals — Convert the fraction part to a decimal and add to the whole number. Example: 3 1/4 = 3 + 0.25 = 3.25.
- Type 4: Fractions giving repeating decimals — Like 1/3 = 0.333... and 2/3 = 0.666... The division never ends.
- Type 5: Improper fractions to decimals — Divide normally. Example: 7/4 = 1.75.
Solved Examples
Example 1: Example 1: Convert 1/2 to Decimal
Problem: Convert 1/2 to a decimal.
Solution (Equivalent Fraction Method):
- Make denominator 10: 2 × 5 = 10.
- Multiply numerator by 5: 1 × 5 = 5.
- 1/2 = 5/10 = 0.5.
Answer: 1/2 = 0.5.
Example 2: Example 2: Convert 3/5 to Decimal
Problem: Convert 3/5 to a decimal.
Solution:
- Make denominator 10: 5 × 2 = 10.
- Multiply numerator by 2: 3 × 2 = 6.
- 3/5 = 6/10 = 0.6.
Answer: 3/5 = 0.6.
Example 3: Example 3: Convert 7/20 to Decimal
Problem: Convert 7/20 to a decimal.
Solution:
- Make denominator 100: 20 × 5 = 100.
- Multiply numerator by 5: 7 × 5 = 35.
- 7/20 = 35/100 = 0.35.
Answer: 7/20 = 0.35.
Example 4: Example 4: Convert 5/8 Using Long Division
Problem: Convert 5/8 to a decimal.
Solution (Division Method):
- 5 ÷ 8:
- 50 ÷ 8 = 6, remainder 2. Write 0.6
- 20 ÷ 8 = 2, remainder 4. Write 0.62
- 40 ÷ 8 = 5, remainder 0. Write 0.625
Answer: 5/8 = 0.625.
Example 5: Example 5: Convert 1/4 to Decimal
Problem: Convert 1/4 to a decimal.
Solution:
- Make denominator 100: 4 × 25 = 100.
- Multiply numerator by 25: 1 × 25 = 25.
- 1/4 = 25/100 = 0.25.
Answer: 1/4 = 0.25.
Example 6: Example 6: Convert Mixed Number 2 3/4 to Decimal
Problem: Convert 2 3/4 to a decimal.
Solution:
- Whole part = 2.
- Fraction part: 3/4 = 0.75 (as we found earlier).
- 2 3/4 = 2 + 0.75 = 2.75.
Answer: 2 3/4 = 2.75.
Example 7: Example 7: Convert 9/25 to Decimal
Problem: Convert 9/25 to a decimal.
Solution:
- Make denominator 100: 25 × 4 = 100.
- Multiply numerator by 4: 9 × 4 = 36.
- 9/25 = 36/100 = 0.36.
Answer: 9/25 = 0.36.
Example 8: Example 8: Convert 7/4 (Improper Fraction) to Decimal
Problem: Convert 7/4 to a decimal.
Solution:
- 7 ÷ 4 = 1, remainder 3. Write 1.
- 30 ÷ 4 = 7, remainder 2. Write 1.7
- 20 ÷ 4 = 5, remainder 0. Write 1.75
Answer: 7/4 = 1.75.
Example 9: Example 9: Convert 1/3 to Decimal
Problem: Convert 1/3 to a decimal.
Solution:
- 1 ÷ 3 = 0.333...
- The digit 3 keeps repeating.
- This is a non-terminating repeating decimal.
Answer: 1/3 = 0.333... or 0.3̄ (the bar over 3 means it repeats).
Example 10: Example 10: Convert 11/50 to Decimal
Problem: Convert 11/50 to a decimal.
Solution:
- Make denominator 100: 50 × 2 = 100.
- Multiply numerator by 2: 11 × 2 = 22.
- 11/50 = 22/100 = 0.22.
Answer: 11/50 = 0.22.
Real-World Applications
Where do we convert fractions to decimals?
- Money — Rs 3/4 is written as Rs 0.75. All money calculations use decimals.
- Measurements — 1/2 inch = 0.5 inch. Measuring tools often show decimals.
- Calculators — Calculators display answers as decimals. Knowing fraction-to-decimal conversion helps you understand the display.
- Percentages — To convert a fraction to a percentage, first convert to decimal, then multiply by 100. Example: 3/4 = 0.75 = 75%.
- Comparing amounts — Which is more: 3/8 of a cake or 2/5? Convert to decimals: 0.375 and 0.4. So 2/5 is more.
- Science — Lab measurements use decimals. If you measure 3/8 of a litre, you record it as 0.375 L.
Key Points to Remember
- To convert a fraction to a decimal, divide the numerator by the denominator.
- The equivalent fraction method works when the denominator can be made 10, 100, or 1000.
- Fractions with denominators 2, 4, 5, 8, 10, 20, 25, 50, 100 give terminating decimals.
- Fractions with denominators 3, 6, 7, 9, 11 often give repeating decimals.
- For mixed numbers, convert the fraction part and add to the whole number.
- Both methods (division and equivalent fraction) give the same answer.
- The equivalent fraction method is quicker when possible.
- Every fraction can be written as either a terminating or repeating decimal.
- Improper fractions give decimals greater than 1.
- Common conversions to remember: 1/2 = 0.5, 1/4 = 0.25, 3/4 = 0.75, 1/5 = 0.2.
Practice Problems
- Convert 3/10 to a decimal.
- Convert 7/8 to a decimal using long division.
- Convert 13/25 to a decimal using the equivalent fraction method.
- Convert the mixed number 4 1/5 to a decimal.
- Which is greater: 5/8 or 7/10? Convert to decimals and compare.
- Convert 2/3 to a decimal. Is it terminating or repeating?
- Convert 11/20 to a decimal.
- A rope is 3 7/8 metres long. Write this as 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. You can also make the denominator 10 or 100 and then write as a decimal.
Q2. What is a terminating decimal?
A terminating decimal is one where the division ends after a fixed number of decimal places. Example: 1/8 = 0.125. The decimal stops (terminates) after three places.
Q3. What is a repeating decimal?
A repeating decimal is one where a digit or group of digits keeps repeating forever. Example: 1/3 = 0.333... The digit 3 repeats without end. It is written as 0.3̄.
Q4. Which fractions give terminating decimals?
Fractions whose denominators (in simplest form) have only 2 and 5 as prime factors give terminating decimals. Examples: 1/2, 1/4, 1/5, 1/8, 1/10, 1/20, 1/25, 1/50, 1/100.
Q5. Can every fraction be written as a decimal?
Yes. Every fraction gives either a terminating decimal or a repeating decimal. There are no other possibilities.
Q6. How do you convert a mixed number to a decimal?
Convert the fraction part to a decimal and add it to the whole number. Example: 5 3/4 = 5 + 0.75 = 5.75.
Q7. Is 0.5 the same as 1/2?
Yes. 1/2 = 1 ÷ 2 = 0.5. They represent the same amount.
Q8. What common fractions should I memorise as decimals?
Useful ones: 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.
