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Basic Percentage Conversion

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Introduction

In aptitude tests, questions often require you to convert between percentages, fractions, and decimals. This is the foundation for all percentage-based problems.

Once you understand these basic conversions, you can solve any percentage problem quickly and with confidence.

Pattern: Basic Percentage Conversion

Pattern: Basic Percentage Conversion

The key idea is to move easily between percentage, fraction, and decimal forms.

Percentage → Fraction: Divide by 100 and simplify.
Fraction → Percentage: Multiply by 100 and add % sign.
Percentage → Decimal: Divide by 100.
Decimal → Percentage: Multiply by 100 and add % sign.

Step-by-Step Example

Question

Convert the following:
(a) 3/8 into percentage
(b) 45% into fraction
(c) 0.25 into percentage

Options:

  • A: (a) 35% , (b) 9/20 , (c) 20%
  • B: (a) 37.5% , (b) 9/20 , (c) 25%
  • C: (a) 40% , (b) 4/9 , (c) 50%
  • D: (a) 33% , (b) 1/2 , (c) 12%

Solution

  1. Step 1: Convert 3/8 into percentage

    Sentence: To convert a fraction into a percentage, multiply it by 100.
    Math: (3/8) × 100 = 37.5%

  2. Step 2: Convert 45% into fraction

    Sentence: To convert percentage into fraction, divide by 100.
    Math: 45% = 45/100 = 9/20

  3. Step 3: Convert 0.25 into percentage

    Sentence: To convert decimal into percentage, multiply by 100.
    Math: 0.25 × 100 = 25%

  4. Final Answer:

    (a) 37.5% , (b) 9/20 , (c) 25% → Option B

  5. Quick Check:

    All conversions match Option B ✔

Quick Variations

Common fractions to remember:

1/2 = 50% , 1/3 = 33.33% , 1/4 = 25% , 1/5 = 20% , 1/8 = 12.5%

Decimals:

0.1 = 10% , 0.2 = 20% , 0.75 = 75%

Trick to Always Use

  • Step 1: % → ÷100 → fraction/decimal
  • Step 2: fraction → ×100 → %
  • Step 3: decimal → ×100 → %
  • Step 4: Remember key fractions for faster solving.

Summary

  • Convert percentages to fractions by dividing by 100.
  • Convert fractions to percentages by multiplying by 100.
  • Convert decimals to percentages by multiplying by 100.
  • Convert percentages to decimals by dividing by 100.

Example to remember:
(a) 3/8 = 37.5%, (b) 45% = 9/20, (c) 0.25 = 25%

Practice

(1/5)
1. Convert 3/8 into percentage.
easy
A. 33.33%
B. 42.5%
C. 37.5%
D. 12.5%

Solution

  1. Step 1: Understand the conversion rule

    To convert a fraction to percentage, multiply by 100.

  2. Step 2: Apply the fraction-to-percentage formula

    (3/8) × 100 = 300/8 = 37.5%.

  3. Final Answer:

    37.5% → Option C

  4. Quick Check:

    1/8 = 12.5% → 3×12.5% = 37.5% ✅
Hint: Remember 1/8 = 12.5% → multiply numerator by 12.5.
Common Mistakes: Dividing by 8 then forgetting to multiply by 100 (order confusion).
2. What is 0.125 expressed as a percentage?
easy
A. 0.125%
B. 12.5%
C. 1.25%
D. 125%

Solution

  1. Step 1: Recall the rule

    To convert a decimal to percentage, multiply by 100.

  2. Step 2: Apply multiplication

    0.125 × 100 = 12.5%.

  3. Final Answer:

    12.5% → Option B

  4. Quick Check:

    0.1 = 10%, 0.025 = 2.5% → total 12.5% ✅
Hint: Move the decimal two places right and add %.
Common Mistakes: Moving decimal only one place (gives 1.25%) or forgetting the % sign.
3. Express 45% as a simplified fraction.
easy
A. 9/20
B. 11/25
C. 1/2
D. 5/9

Solution

  1. Step 1: Convert percentage to fraction

    Write 45% as 45/100.

  2. Step 2: Simplify the fraction

    Divide numerator and denominator by 5 → 45/100 = 9/20.

  3. Final Answer:

    9/20 → Option A

  4. Quick Check:

    9/20 = 0.45 → 0.45×100 = 45% ✅
Hint: Reduce 45/100 by GCD (5) to get 9/20 quickly.
Common Mistakes: Leaving as 45/100 instead of simplifying to 9/20.
4. Which decimal equals 7.5% ?
medium
A. 0.75
B. 0.0075
C. 7.5
D. 0.075

Solution

  1. Step 1: Convert percentage to decimal

    Divide percentage by 100.

  2. Step 2: Apply conversion

    7.5% = 7.5 ÷ 100 = 0.075.

  3. Final Answer:

    0.075 → Option D

  4. Quick Check:

    0.075×100 = 7.5% ✅
Hint: Move decimal two places left to go from % to decimal.
Common Mistakes: Moving decimal the wrong way (0.75 would be 75%).
5. Convert the fraction 7/16 into percentage (exact).
medium
A. 43.75%
B. 41.25%
C. 38.50%
D. 46.00%

Solution

  1. Step 1: Use the fraction-to-percentage rule

    Multiply the fraction by 100.

  2. Step 2: Calculate precisely

    (7/16) × 100 = 700/16 = 43.75%.

  3. Final Answer:

    43.75% → Option A

  4. Quick Check:

    1/16 = 6.25% → 7×6.25% = 43.75% ✅
Hint: Know 1/16 = 6.25% and multiply by numerator.
Common Mistakes: Arithmetic slip dividing 700 by 16 incorrectly.