How do you convert a percent with a decimal in it, like 6.5%, to a decimal?

Apply the same rule — divide by 100 by moving the decimal point two places to the left. So 6.5% becomes 0.065. The extra digit just means you need to add a leading zero.

Converting Percents and Decimals — Definition, Formula & Examples

Converting percents and decimals is the process of rewriting a percent as a decimal or a decimal as a percent. Since "percent" means "per hundred," you divide by 100 to go from percent to decimal and multiply by 100 to go from decimal to percent.

A percent $p\%$ represents the ratio $\frac{p}{100}$ . To express $p\%$ as a decimal, compute $p \div 100$ . Conversely, to express a decimal $d$ as a percent, compute $d \times 100$ and append the percent symbol. These operations are equivalent to shifting the decimal point two places left or right, respectively.

Key Formula

p\% = \frac{p}{100} = p \div 100 \qquad \text{and} \qquad d = d \times 100\%

Where:

$p$ = The numeric value of the percent (e.g., 45 in 45%)
$d$ = The decimal value being converted to a percent

How It Works

The key idea is that "percent" literally means "out of 100," so every percent is a fraction with a denominator of 100. To convert a percent to a decimal, move the decimal point two places to the left (dividing by 100). To convert a decimal to a percent, move the decimal point two places to the right (multiplying by 100) and add the % symbol. This works for any number — whole numbers, fractions, or decimals that are already in percent form like 12.5%.

Worked Example

Problem: Convert 75% to a decimal.

Step 1: Write the percent as a division by 100.

75\% = 75 \div 100

Step 2: Move the decimal point two places to the left.

75. \rightarrow 0.75

Step 3: State the result.

75\% = 0.75

Answer: 75% = 0.75

Another Example

Problem: Convert 0.4 to a percent.

Step 1: Multiply the decimal by 100.

0.4 \times 100 = 40

Step 2: This is equivalent to moving the decimal point two places to the right.

0.4 \rightarrow 40.

Step 3: Attach the percent symbol.

0.4 = 40\%

Answer: 0.4 = 40%

Visualization

Why It Matters

You will use percent-decimal conversions constantly in pre-algebra and algebra courses whenever you solve problems involving discounts, tax, interest rates, or probability. In everyday life, comparing a sale price of 30% off to a decimal multiplier of 0.70 is exactly this skill. Standardized tests like state assessments and the SAT expect you to move fluently between these two forms.

Common Mistakes

Mistake: Moving the decimal point in the wrong direction — for example, writing 5% as 5.00 instead of 0.05.

Correction: Remember: percent to decimal means dividing by 100, so the number gets smaller. Move the decimal point two places to the left.

Mistake: Forgetting to move the decimal point the full two places, turning 8% into 0.8 instead of 0.08.

Correction: Always shift exactly two places. If needed, fill in a zero as a placeholder: 8% → 08. → 0.08.

Related Terms

Decimal — One of the two forms in this conversion
Fraction — Percents can also be written as fractions
Ratio — A percent is a ratio out of 100
Denominator — Percent fractions always have denominator 100
Numerator — The percent value becomes the numerator over 100
Fraction Rules — Rules for simplifying percent fractions