Fractions, Decimals & Percents

Fractions, decimals, and percents are three ways to write the same amount. In this lesson you'll explore how they match up, learn a step-by-step method for switching between them, handle amounts that don't come out even, and learn to compare mixed forms. Then you'll practice with three activities.

New to percents? Start with Understanding Percents.

Three Names for One Amount

Picture one whole cut into equal parts. You can describe how much is shaded as a fraction (how many parts out of how many), as a decimal (a place-value number), or as a percent (how many out of 100). The amount does not change. Only the way we write it changes.

Drag the slider or pick a fraction. Watch all three forms change together.

The Amount Explorer

The whole strip is 1 whole = 1 = 100%

As a fraction

As a decimal

As a percent

Notice: The fraction is always shown in simplest form, so the number of parts changes as you slide. The strip is cut into 4 parts at 25%, but into 100 parts at 37%. The decimal and the percent stay tied to the same spot on the strip.

Converting, Step by Step

There are six ways to switch between the three forms. Here is the whole map:

Fraction

→ Divide the top by the bottom

← Read the place value, then simplify

Decimal

0.375

→ Move the point 2 places right

← Move the point 2 places left

Percent

37.5%

To go between a fraction and a percent, you can travel through the decimal, or write the percent over 100 and simplify.

The Conversion Stepper

Pick an amount and a route. Then reveal one step at a time.

1. Pick an amount

2. Pick a route

Always check: Does your answer make sense? Half is 1/2 = 0.5 = 50%. If your fraction is less than half, your decimal should be less than 0.5 and your percent less than 50%. Try the last step in the stepper on a few different amounts.

Want more practice with just fractions and decimals? Try Converting Fractions & Decimals.

Amounts That Don't Come Out Even

Some fractions turn into decimals that never end. Dividing 1 by 3 gives 0.3333… with the 3 repeating forever. A bar over the digit shows what repeats, like this: 0.3.

Fraction	Decimal	Percent
	0.3	33.3%
	0.6	66.6%
	0.16	16.6%
	0.83	83.3%
	0.1	11.1%

We can't write a decimal that goes on forever, so we round. Try it:

The Rounding Machine

Choose a fraction and a place to round to.

Fraction

Round to the nearest…

Two symbols: The = sign means exactly equal. The ≈ sign means "about equal." Since 1/3 is 33.333…%, we write 1/3 ≈ 33.3%. You may also see it written exactly as 33⅓%.

Comparing Mixed Forms

Which is greater: , 0.6, or 55%? You can't compare them until they are written the same way. Pick one form, change everything to it, and then compare. Percents are often the easiest form to choose.

Compare 5/8, 0.6, and 55%

Step 1. Change every amount to a percent.

= 0.625 = 62.5%

62.5%

0.6 = 60%

60%

55%

55%

Step 2. Compare the percents: 55% < 60% < 62.5%.

So, from least to greatest: 55%, 0.6, .

Which form should you use? Each one is useful in different places:

Fractions

Sharing equal parts, recipes, and measurements, like 3/4 of a cup.

Decimals

Money, metric measurements, and anything on a calculator, like $0.75.

Percents

Comparing different wholes: test scores, sales, and statistics, like 75% off.

Comparing decimals? Line up the decimal points and add zeros so they have the same number of places: 0.6, 0.55, and 0.625 become 0.600, 0.550, and 0.625. The digits don't lie. 625 > 600 > 550.

Let's Practice

Three activities: type your own conversions, compare amounts written in different forms, and put mixed amounts in order.

Convert It

Change each amount to the form asked for, then type your answer. No need to type the % sign.

Question 1 of 10Score: 0

Which Is Greater?

The two amounts are written in different forms. Decide which is greater, or whether they are equal.

Question 1 of 10Score: 0

Which is greater?

Put in Order

Tap the amounts one at a time, from least to greatest. Tap a filled box to take it (and everything after it) back.

Round 1 of 6Score: 0

Amounts

LeastGreatest

What's next? Now that you can move easily between fractions, decimals, and percents, you're ready to use percents to solve problems, like finding 20% of a number. That's where percents really come to life!