Converting Decimals to Percentage
Converting decimals to percentage is a quick and simple process. Since percentage means "out of 100," and decimals already use place values based on powers of 10, the conversion involves just one step — multiply by 100.
For example, 0.45 = 45%. The decimal 0.45 means 45 hundredths, which is exactly 45 out of 100 — and that is what 45% means.
This skill is useful when reading data, interpreting results, and working with real-life quantities like exam scores, discounts, probability, sports averages, and statistics. When a news report says "0.65 of people surveyed agreed," you can immediately convert: 0.65 = 65% agreed.
In this topic, you will learn how to convert any decimal — whether it is less than 1, equal to 1, or greater than 1 — to a percentage. You will also understand why this conversion works using place value reasoning.
What is Converting Decimals to Percentage - Class 5 Maths (Percentage)?
A decimal expresses a value using a decimal point and place values (tenths = 1/10, hundredths = 1/100, thousandths = 1/1000, etc.).
A percentage expresses a value as parts per hundred, using the % symbol.
Converting a decimal to a percentage means expressing the decimal as a number out of 100.
Decimal to Percentage: Multiply the decimal by 100 and add %
Why does multiplying by 100 work?
The decimal 0.45 means 45/100 (forty-five hundredths). Since percentage means "per hundred," 45 hundredths = 45 per hundred = 45%. Multiplying by 100 converts the decimal representation into the "per hundred" count.
Mechanically, multiplying by 100 simply moves the decimal point two places to the right:
- 0.45 → move two places right → 45 → 45%
- 0.7 → move two places right → 70 → 70%
- 0.08 → move two places right → 8 → 8%
Converting Decimals to Percentage Formula
Percentage = Decimal × 100
Step-by-step method:
- Take the decimal number.
- Multiply it by 100 (or equivalently, move the decimal point 2 places to the right).
- Write the result with the % symbol.
Examples of the shortcut:
| Decimal | Move Decimal 2 Places Right | Percentage |
|---|---|---|
| 0.5 | 0.50 → 50 | 50% |
| 0.35 | 0.35 → 35 | 35% |
| 0.08 | 0.08 → 8 | 8% |
| 0.125 | 0.125 → 12.5 | 12.5% |
| 1.5 | 1.50 → 150 | 150% |
Reverse operation (Percentage to Decimal):
Divide the percentage by 100 (move decimal two places left). For example, 45% ÷ 100 = 0.45.
Types and Properties
Type 1: Decimals between 0 and 1 (percentages from 0% to 100%)
These are the most common. The resulting percentage is between 0% and 100%.
- 0.5 = 50% (half)
- 0.25 = 25% (one quarter)
- 0.75 = 75% (three quarters)
- 0.1 = 10% (one tenth)
- 0.08 = 8%
Type 2: Decimal equal to 1 (100%)
- 1.0 = 100% (the complete whole)
Type 3: Decimals greater than 1 (percentages above 100%)
When the value exceeds the whole, the percentage is more than 100%.
- 1.5 = 150% (one and a half times the whole)
- 2.0 = 200% (double the whole)
- 1.25 = 125%
- 3.5 = 350%
Type 4: Very small decimals (percentages less than 10%)
Small fractions produce small percentages.
- 0.05 = 5%
- 0.01 = 1%
- 0.005 = 0.5% (half of one percent)
- 0.001 = 0.1%
Type 5: Decimals with three or more places
The percentage may itself contain a decimal point.
- 0.125 = 12.5%
- 0.333 = 33.3%
- 0.875 = 87.5%
Solved Examples
Example 1: Simple Conversion — 0.6
Problem: Convert 0.6 to a percentage.
Solution:
Step 1: Multiply by 100: 0.6 × 100 = 60
Step 2: Add the % symbol.
Place value explanation: 0.6 = 6 tenths = 60 hundredths = 60%
Answer: 0.6 = 60%
Example 2: Two Decimal Places — 0.35
Problem: Convert 0.35 to a percentage.
Solution:
Step 1: Multiply by 100: 0.35 × 100 = 35
Step 2: Add %.
Place value explanation: 0.35 = 35 hundredths = 35 out of 100 = 35%
Answer: 0.35 = 35%
Example 3: Small Decimal — 0.04
Problem: Convert 0.04 to a percentage.
Solution:
Step 1: Multiply by 100: 0.04 × 100 = 4
Step 2: Add %.
Note: 0.04 is a small number — just 4 hundredths, which equals 4%.
Answer: 0.04 = 4%
Example 4: Decimal Greater Than 1 — 1.35
Problem: Convert 1.35 to a percentage.
Solution:
Step 1: Multiply by 100: 1.35 × 100 = 135
Step 2: Add %.
What does 135% mean? It means 135 out of 100 — more than the whole. If a price was ₹100 and it became ₹135, the new price is 135% of the original.
Answer: 1.35 = 135%
Example 5: Word Problem — Quiz Score
Problem: Kavi's score on a quiz was 0.85 (out of a maximum of 1). Express his score as a percentage.
Solution:
Step 1: The score 0.85 is out of 1 (the maximum). To express as percentage: 0.85 × 100 = 85.
Step 2: Add %.
Meaning: Kavi answered correctly on 85 out of every 100 questions (if there were 100).
Answer: Kavi scored 85%.
Example 6: Word Problem — Rainfall Data
Problem: A weather report says 0.7 of the days in June had rain. What percentage of days had rain?
Solution:
Step 1: 0.7 × 100 = 70
Step 2: Add %.
Context: If June has 30 days, then 0.7 × 30 = 21 days had rain. That is 21 out of 30 = 70%.
Answer: 70% of days in June had rain.
Example 7: Three Decimal Places — 0.125
Problem: Convert 0.125 to a percentage.
Solution:
Step 1: Multiply by 100: 0.125 × 100 = 12.5
Step 2: Add %.
Note: The resulting percentage (12.5%) itself has a decimal. This is perfectly normal. 0.125 = 1/8, and 1/8 of 100 = 12.5.
Answer: 0.125 = 12.5%
Example 8: Decimal Equal to 1
Problem: Convert 1.0 to a percentage.
Solution:
Step 1: 1.0 × 100 = 100
Step 2: Add %.
Meaning: 1.0 represents the entire quantity — the whole. 100% means all of it, nothing missing.
Answer: 1.0 = 100%
Example 9: Word Problem — Shopping Savings
Problem: A shopkeeper tells Aditi she saved 0.15 of her total bill. Express this saving as a percentage.
Solution:
Step 1: 0.15 × 100 = 15
Step 2: Add %.
Real-life meaning: For every ₹100 of the bill, Aditi saved ₹15. If her bill was ₹800, she saved 0.15 × 800 = ₹120.
Answer: Aditi saved 15% of her bill.
Example 10: Common Decimals to Percentages — Reference Table
Problem: Convert each decimal to a percentage: 0.1, 0.25, 0.5, 0.75, 0.9, 1.0, 1.5.
Solution:
| Decimal | × 100 | Percentage | Meaning |
|---|---|---|---|
| 0.1 | 10 | 10% | One tenth |
| 0.25 | 25 | 25% | One quarter |
| 0.5 | 50 | 50% | Half |
| 0.75 | 75 | 75% | Three quarters |
| 0.9 | 90 | 90% | Nine tenths |
| 1.0 | 100 | 100% | The whole |
| 1.5 | 150 | 150% | One and a half |
Tip: Memorise the common conversions. They help with quick mental calculations.
Real-World Applications
Where do we convert decimals to percentages in real life?
- Exam scores: A score of 0.92 out of 1 = 92%. Teachers and students use percentages to report and understand results.
- Probability: A 0.3 chance of rain tomorrow = 30% chance. Weather apps display percentages.
- Sports: A cricketer's batting average of 0.45 = 45% success rate. Sports commentators convert to percentages for clarity.
- Data analysis and surveys: If 0.6 of survey respondents agree with a statement, that is 60% agreement. Easier to understand than 0.6.
- Nutrition labels: "0.02 of daily value" on a food packet means 2% of your daily requirement.
- Battery and downloads: Your phone shows "battery 0.45" as 45%. A download at 0.8 complete shows as 80%.
- Financial reports: Growth of 0.05 in a company's revenue means 5% growth.
Key Points to Remember
- To convert a decimal to a percentage, multiply by 100 and add the % symbol.
- Multiplying by 100 is the same as moving the decimal point two places to the right.
- Key benchmarks: 0.01 = 1%, 0.1 = 10%, 0.25 = 25%, 0.5 = 50%, 0.75 = 75%, 1.0 = 100%.
- Decimals between 0 and 1 give percentages between 0% and 100%.
- Decimals greater than 1 give percentages greater than 100% (e.g., 1.5 = 150%).
- Very small decimals like 0.005 give percentages less than 1% (0.5%).
- This conversion is the reverse of percentage-to-decimal (where you divide by 100).
- The conversion works because "percent" literally means "per hundred" — multiplying by 100 gives the count per hundred.
- The percentage result itself can contain a decimal (e.g., 0.125 = 12.5%).
Practice Problems
- Convert 0.45 to a percentage.
- Convert 0.8 to a percentage.
- Express 0.07 as a percentage.
- Aditi completed 0.9 of her homework. What percentage has she completed?
- Convert 1.6 to a percentage.
- A plant grew 0.375 m in a week. Express this growth as a percentage of 1 m.
- Convert 0.005 to a percentage.
- Rahul saved 0.2 of his pocket money each month. What percentage does he save?
Frequently Asked Questions
Q1. How do you convert a decimal to a percentage?
Multiply the decimal by 100 and write the % sign. For example, 0.72 × 100 = 72, so 0.72 = 72%. You can also think of it as moving the decimal point two places to the right.
Q2. Why do we multiply by 100 to get a percentage?
Because percentage means 'per hundred.' A decimal like 0.45 means 45 hundredths. Multiplying by 100 converts this to 45 per hundred, which is 45%.
Q3. What is 0.5 as a percentage?
0.5 × 100 = 50. So 0.5 = 50%, which means half.
Q4. Can a decimal greater than 1 be converted to a percentage?
Yes. Decimals greater than 1 give percentages greater than 100%. For example, 1.5 × 100 = 150%, and 2.0 × 100 = 200%. This means the value is more than the original whole.
Q5. What is 0.01 as a percentage?
0.01 × 100 = 1. So 0.01 = 1%, which means 1 part out of 100. It is a very small portion.
Q6. How do you convert a percentage back to a decimal?
Divide the percentage by 100 (move the decimal two places left). For example, 45% ÷ 100 = 0.45. This is the exact reverse of decimal-to-percentage conversion.
Q7. Is moving the decimal point two places right the same as multiplying by 100?
Yes, they are the same operation. Moving the decimal point two places to the right multiplies the number by 100. For example, 0.35 → 35 = 35%.
Q8. What percentage does the decimal 0 represent?
0 × 100 = 0. So the decimal 0 equals 0%, meaning none of the quantity. If 0% of students were absent, nobody was absent.
Q9. How are decimals, fractions, and percentages connected?
They are three different ways to write the same value. For example: 0.75 = 3/4 = 75%. To go from decimal to percentage, multiply by 100. To go from fraction to percentage, divide numerator by denominator then multiply by 100.
