How to Convert Between Percents and Decimals: Step-by-Step Guide
The relationship between Percent and Decimals Relation Formulas is a key concept in maths, especially for students preparing for exams or applying maths to real-life problems. Understanding how to convert between percents and decimals helps you solve questions in arithmetic, algebra, and statistics quickly and accurately.
Understanding Percent and Decimal Conversion
A percent (%) is a way to express a number as a part of 100. For example, 25% means 25 out of 100. A decimal, on the other hand, expresses numbers using the base 10 system, like 0.25. Both are different ways to show the same value. Mastering this conversion is important in maths and everyday life—whether it’s calculating discounts, interest rates, or exam scores.
Percent and Decimal Relation Formulas
The core formulas are simple:
- To convert percent to decimal: Divide by 100 (x % = x/100).
- To convert decimal to percent: Multiply by 100 and add the % sign (x = x × 100 %).
| Conversion | Formula | Example |
|---|---|---|
| Percent to Decimal | Decimal = Percent ÷ 100 | 12.5% = 12.5 ÷ 100 = 0.125 |
| Decimal to Percent | Percent = Decimal × 100 % | 0.04 × 100 = 4% |
Step-by-Step Worked Examples
Example 1: Convert Percent to Decimal
Convert 8.875% to a decimal.
- Write as a fraction: 8.875 ÷ 100
- Calculate: 8.875 ÷ 100 = 0.08875
Example 2: Convert Decimal to Percent
Convert 0.007 to percent.
- Multiply by 100: 0.007 × 100 = 0.7
- Add the percent sign: 0.7%
Example 3: Special Case – More than 100%
Convert 125% to decimal.
- 125 ÷ 100 = 1.25
Example 4: Recurring Decimal
Convert 33.33% to a decimal.
- 33.33 ÷ 100 = 0.3333 (recurring decimal)
Example 5: Decimal Greater than 1
Convert 2.5 to percent.
- 2.5 × 100 = 250%
Practice Problems
- Convert 16% to decimal.
- Express 0.12 as a percent.
- What is 2.75% as a decimal?
- Change 0.402 to a percent.
- Convert 87.5% to decimal.
- Write 1.1 as a percent.
- Express 92% as a decimal.
- What is 0.003 as a percent?
- Convert 150% to decimal.
- Express 0.045 as a percent.
Common Mistakes to Avoid
- Moving the decimal point in the wrong direction (remember: left for percent to decimal, right for decimal to percent).
- Forgetting to add the percent sign (%) when converting from decimal to percent.
- Incorrectly dividing or multiplying by 100—be careful with placement of zeros and decimal points.
- Mixing up percent and percent value (for example, writing 0.5% as 0.5 instead of 0.005).
Real-World Applications
Percent to decimal conversions are everywhere:
- Shopping discounts: 20% off = 0.2 × original price
- Bank interest rates: 7.5% annual rate = 0.075
- Exam results: 85% scored = 0.85 of total marks
- Percentage word problems in competitive exams and Olympiads
At Vedantu, we show how these simple conversions make complicated problems much easier to solve, both in school questions and daily life.
You can also use our percent and decimal calculator online, or download a fraction decimal percent chart for instant reference.
Page Summary
This page explained the percent and decimals relation formulas and showed how easy it is to convert between percent and decimals using simple rules and examples. Recognising this relationship is essential for quick calculations in maths, exams, and real-world decisions. Keep practicing these conversions and explore more related topics like Fractions and Decimals or Decimal to Percent on Vedantu for more confidence and success.
FAQs on Percent and Decimal Conversion: Formulas, Tips & Practice
1. What is the relationship between percents and decimals?
Percentages and decimals are two different ways to represent parts of a whole. A percentage shows a proportion out of 100, while a decimal represents a fraction where the denominator is a power of 10. They are directly related: 100% is equal to 1.0 (or 1), 1% is 0.01, etc. Converting between them involves simple multiplication or division by 100.
2. How do you convert a percent to a decimal (and vice versa)?
To convert a percent to a decimal, divide the percentage by 100 (or move the decimal point two places to the left). To convert a decimal to a percent, multiply the decimal by 100 (or move the decimal point two places to the right) and add a % sign. This is a fundamental concept in arithmetic and number operations.
3. What is 8.875% as a decimal?
To convert 8.875% to a decimal, divide 8.875 by 100. This gives you 0.08875. This is a common conversion used in many calculations involving percentages and decimals.
4. What is 12.5% as a decimal?
12.5% as a decimal is 0.125. Divide 12.5 by 100 to find this answer. This is a frequently used conversion in arithmetic problems involving percentages and decimal numbers.
5. How do you convert a decimal greater than 1 to a percent?
Converting a decimal greater than 1 to a percentage is done the same way as with decimals less than 1: multiply by 100 and add the % symbol. For example, 1.25 becomes 125%. This is important for understanding percentage increases that are greater than the original value.
6. What is the formula to convert percent to decimal?
The formula for converting a percentage to a decimal is: Decimal = Percentage ÷ 100. Remember to always divide by 100 when converting from percent to decimal form. This is a key formula for solving percentage problems.
7. What is the formula to convert decimal to percent?
To convert a decimal to a percentage, use the formula: Percentage = Decimal × 100. Always multiply by 100 and add a % sign to show the result as a percentage. This formula is essential in arithmetic and understanding number operations.
8. How to convert 25.2% in decimal form?
To express 25.2% as a decimal, divide 25.2 by 100, resulting in 0.252. This is a simple application of the percent to decimal conversion rule.
9. What if the percent is over 100%?
Percentages over 100% represent values greater than the original whole. The conversion to decimals remains the same: divide by 100. For instance, 150% is equal to 1.5. Understanding this is crucial for analyzing growth rates or increases that exceed the original amount.
10. How do recurring decimals behave when converted to percentages?
Recurring decimals, when converted to percentages, will still retain their recurring nature. For example, 0.333... (recurring) becomes 33.333...% (recurring). The conversion process doesn't change the repeating pattern of the digits.
11. Are there situations where percentages above 100% are meaningful, and how does the conversion work there?
Yes, percentages above 100% are meaningful in situations indicating growth, increase, or exceeding a base value. For instance, a 120% increase means the value is 1.2 times larger. The conversion to decimals follows the same rule: divide the percentage by 100. For example, 120% is equal to 1.2 in decimal form.
