Lesson 48: Fraction-Decimal-Percent Equivalents

New Concept

We may describe part of a whole using a fraction, a decimal, or a percent. To convert a fraction or a decimal to a percent, we multiply the number by $100\%$.

What’s next

This is just the beginning. Next, you'll tackle worked examples and complete a table to solidify your understanding of these conversions.

Property

To change a fraction to its percent equivalent, you simply multiply the fraction by $100\%$.

Examples

$\frac{7}{10} \times 100\% = \frac{700\%}{10} = 70\%$
$\frac{2}{3} \times 100\% = \frac{200\%}{3} = 66\frac{2}{3}\%$

Explanation

Think of this as a "percent-inator" ray gun! You zap a fraction with the $100\%$ beam, and it instantly transforms into its percentage form. This makes it super easy to see how many pieces out of a hundred the fraction represents, which is great for comparing different amounts.

Property

To change a decimal to its percent equivalent, multiply the number by $100\%$.

Examples

$0.8 \times 100\% = 80\%$
$1.5 \times 100\% = 150\%$
$0.04 \times 100\% = 4\%$

Explanation

Multiplying a decimal by $100\%$ is like a superpower promotion! It moves the decimal point two places to the right and slaps a percent sign on the end. It's the fastest way to see the 'parts per hundred' value of any decimal, turning it into a grade-A superhero of numbers.

Property

To convert a percent, remember that 'percent' means 'out of 100'. So, $x\% = \frac{x}{100}$.

Examples

$60\% = \frac{60}{100} = \frac{3}{5}$
$60\% = \frac{60}{100} = 0.6$
$150\% = \frac{150}{100} = 1\frac{1}{2} = 1.5$

Explanation

Think of a percent as a disguise! To reveal its true fraction or decimal identity, you just unmask it. The percent sign (\%) is a secret code for "divide by 100." Once you do that, you've got a fraction! From there, you can easily find the decimal form by just dividing.