Converting Between Fractions, Decimals, and Percents

Fractions, decimals, and percents are three ways to write the same value. A test score of $\frac{4}{5}$, the decimal $0.8$, and $80$% all mean the same thing. Being able to convert fluently between these forms is one of the most practical math skills you can have — it shows up in shopping, cooking, healthcare, construction, and nearly every standardized test.

The Conversion Roadmap

Here is the quick-reference chart for all six conversions:

The rest of this page walks through each conversion with examples. For the foundational arithmetic behind these concepts, see Decimals and Percentages.

Fraction to Decimal

Method: Divide the numerator by the denominator.

Example 1: Convert $\frac{3}{8}$ to a decimal

$3 \div 8 = 0.375$

Example 2: Convert $\frac{5}{6}$ to a decimal

$5 \div 6 = 0.8333... = 0.8\overline{3}$

This is a repeating decimal. When a fraction’s denominator has prime factors other than 2 and 5, the decimal will repeat. For practical purposes, round to the needed precision: $0.833$ or $0.83$.

Example 3: Convert $\frac{7}{4}$ to a decimal

$7 \div 4 = 1.75$

Improper fractions produce decimals greater than 1.

Decimal to Fraction

Method: Read the decimal as a fraction based on place value, then simplify.

Example 4: Convert $0.6$ to a fraction

The 6 is in the tenths place:

$0.6 = \frac{6}{10} = \frac{3}{5}$

Example 5: Convert $0.45$ to a fraction

The last digit is in the hundredths place:

$0.45 = \frac{45}{100} = \frac{9}{20}$

Example 6: Convert $0.125$ to a fraction

The last digit is in the thousandths place:

$0.125 = \frac{125}{1000} = \frac{1}{8}$

Simplify by dividing numerator and denominator by 125.

Handling Repeating Decimals

For $0.\overline{3}$ (the 3 repeats forever), you may recall that this equals $\frac{1}{3}$. For $0.\overline{6}$, this equals $\frac{2}{3}$. The common repeating decimals are worth memorizing (see the equivalents table below).

Decimal to Percent

Method: Multiply by 100, which is the same as moving the decimal point two places to the right.

Example 7: Convert $0.72$ to a percent

$0.72 \times 100 = 72$%

Example 8: Convert $0.035$ to a percent

$0.035 \times 100 = 3.5$%

Example 9: Convert $1.5$ to a percent

$1.5 \times 100 = 150$%

Decimals greater than 1 convert to percents greater than 100%.

Percent to Decimal

Method: Divide by 100, which is the same as moving the decimal point two places to the left.

Example 10: Convert $45$% to a decimal

$45 \div 100 = 0.45$

Example 11: Convert $6.5$% to a decimal

$6.5 \div 100 = 0.065$

Example 12: Convert $200$% to a decimal

$200 \div 100 = 2.0$

Fraction to Percent

Method 1 — Decimal bridge: Convert the fraction to a decimal, then multiply by 100.

Method 2 — Proportion: Set up $\frac{\text{part}}{\text{whole}} = \frac{x}{100}$ and solve for $x$.

Example 13: Convert $\frac{3}{5}$ to a percent

Decimal bridge: $3 \div 5 = 0.6$, and $0.6 \times 100 = 60$%.

Proportion: $\frac{3}{5} = \frac{x}{100}$. Cross-multiply: $5x = 300$, so $x = 60$%.

Both methods give $60$%.

Example 14: Convert $\frac{7}{8}$ to a percent

$7 \div 8 = 0.875$, and $0.875 \times 100 = 87.5$%.

Percent to Fraction

Method: Write the percent over 100, then simplify.

Example 15: Convert $75$% to a fraction

$\frac{75}{100} = \frac{3}{4}$

Example 16: Convert $12.5$% to a fraction

$\frac{12.5}{100} = \frac{125}{1000} = \frac{1}{8}$

Multiply numerator and denominator by 10 to clear the decimal, then simplify.

Common Equivalents Table

Memorizing these common conversions saves time on tests and in daily life.

Real-World Application: Retail — Comparing Discounts

A store offers two coupons: one for $\frac{1}{3}$ off and another for $30$% off. Which saves more money?

Convert $\frac{1}{3}$ to a percent: $1 \div 3 = 0.\overline{3}$, and $0.\overline{3} \times 100 = 33.\overline{3}$%.

Since $33.\overline{3}$% is greater than $30$%, the $\frac{1}{3}$-off coupon saves more. On a $60 item, the difference is:

• $\frac{1}{3}$ off: $60 $\times$ $0.\overline{3}$ = $20 saved
• $30$% off: $60 $\times$ $0.30$ = $18 saved

The fraction coupon saves $2 more.

Real-World Application: Nursing — Reading Lab Results

A lab report shows a patient’s hematocrit as $0.42$. The nurse needs to chart this as a percentage.

$0.42 \times 100 = 42$%

The patient’s hematocrit is $42$%, which falls within the normal range ($36$%–$48$% for women, $40$%–$54$% for men). Being able to move between decimal and percent forms is essential for interpreting lab values correctly.

Common Mistakes to Avoid

1. Moving the decimal the wrong direction. Decimal to percent: move right 2 places (multiply by 100). Percent to decimal: move left 2 places (divide by 100). Mixing these up is extremely common.

2. Forgetting to simplify the fraction. $0.4 = \frac{4}{10}$, but the simplified answer is $\frac{2}{5}$.

3. Confusing $0.05$ with $5$% and $50$%. Practice: $0.05 = 5$%, $0.5 = 50$%, $5 = 500$%. Always double-check by asking: “Is this value less than 1, equal to 1, or greater than 1?”

4. Rounding repeating decimals too aggressively. $\frac{1}{3} = 0.333...$, not $0.3$. When precision matters (as in nursing or finance), carry enough decimal places or use the fraction form.

5. Not recognizing common equivalents. Knowing that $\frac{3}{4} = 0.75 = 75$% by heart saves time and reduces errors.

Practice Problems

Test your conversion skills. Click to reveal each answer.

Key Takeaways

• Fraction to decimal: divide numerator by denominator
• Decimal to percent: multiply by 100 (move decimal 2 places right)
• Percent to decimal: divide by 100 (move decimal 2 places left)
• Percent to fraction: write over 100, then simplify
• Memorize the common equivalents — they appear constantly in real life and on tests
• Converting between forms is not just a classroom exercise; it is how you compare discounts, interpret medical data, and communicate quantities clearly

Return to Pre-Algebra for more topics in this section.