Which way does the decimal point move when converting percents?

Percent to decimal moves the point two places left (you divide by 100), and decimal to percent moves it two places right (you multiply by 100). Anchor the rule to a fact you know for sure: 50% is one half, which is 0.5, so 50 must shrink when the percent symbol comes off.

Can a percent be larger than 100 or smaller than 1?

Yes to both. 250\% means 2.5 times the whole, which shows up in growth, markups, and comparisons. And 0.4\% means four tenths of one percent, or 0.004 as a decimal — useful for very small rates. Only percents describing a part of a single whole are limited to the range from 0 to 100.

Should I round a repeating decimal or keep the fraction?

Keep the fraction whenever you need an exact answer or plan to multiply and divide further, because 0.33 is not exactly 1/3. Round the decimal only for comparing or reporting, and show that it is approximate: 1/3 = 0.3 0.33.

M7MATH-1.4

Converting Fractions, Decimals & Percents

Learn to convert fractions, decimals, and percents in Grade 7: divide for terminating or repeating decimals, shift by 100 for percents, and simplify a percent over 100.

What you'll do in this lesson

A voice-first session with the Crimsora tutor on Converting Fractions, Decimals & Percents, then targeted practice and FRQs — with the tutor adapting to where you get stuck.

Start Converting Fractions, Decimals & Percents free

What this lesson covers

A test score of 0.85, a fraction of

\frac{17}{20}

, and a percent of 85% all describe exactly the same amount — they are just three different outfits on the same number. Being able to switch outfits quickly is one of the most useful skills in Grade 7, because some problems are easier with fractions (multiplying), some are easier with decimals (adding money or measurements), and some are easier with percents (comparing sizes, discounts, and data).

In this lesson you will practice three moves: dividing the numerator by the denominator to turn a fraction into a terminating or repeating decimal, multiplying or dividing by 100 to cross between a decimal and a percent, and writing a percent over 100 and simplifying it back to a fraction. Along the way you will learn where students most often slip — usually by moving the decimal point the wrong direction.

Three Names for One Number

Every rational number can be written as a fraction, as a decimal, and as a percent. The word percent literally means "per hundred," so a percent is really a fraction with a hidden denominator of 100. That single fact drives every conversion in this lesson.

\frac{3}{4} = 0.75 = 75\% = \frac{75}{100}

Think of a triangle with fraction, decimal, and percent at the corners. There are six trips you can take around it, but only three tools you need to learn:

Trip	Tool
Fraction to decimal	Divide numerator by denominator
Decimal to fraction	Read the place value, then simplify
Decimal to percent	Multiply by 100 (point moves 2 right)
Percent to decimal	Divide by 100 (point moves 2 left)
Percent to fraction	Write over 100, simplify
Fraction to percent	Divide first, then multiply by 100

Notice the last trip is really two trips joined together. There is a shortcut when the denominator divides evenly into 100: scale the fraction up so the denominator is 100, and the numerator becomes the percent. For example

\frac{7}{20} = \frac{35}{100} = 35\%

because

20 \times 5 = 100

and

7 \times 5 = 35

. That shortcut only works for denominators like 2, 4, 5, 10, 20, 25, and 50. For anything else — 3, 7, 8, 16 — just divide.

Dividing a Fraction: Terminating or Repeating

A fraction bar is a division sign. To write

\frac{5}{8}

as a decimal, divide 5 by 8. Set it up as

5.000 \div 8

, adding zeros after the decimal point as needed, and you get

0.625

. The division ended with a remainder of 0, so

0.625

is a terminating decimal.

Sometimes the division never ends. Dividing

1 \div 3

gives

0.3333\ldots

, and the same remainder of 1 keeps coming back forever. That is a repeating decimal, and mathematicians write it with a bar over the digits that repeat:

\frac{1}{3} = 0.\overline{3}

. For

\frac{5}{11}

you get

0.454545\ldots = 0.\overline{45}

, with the bar covering both digits. For

\frac{1}{6}

you get

0.1666\ldots = 0.1\overline{6}

— the 1 does not repeat, so the bar sits only over the 6.

Here is the tidy pattern: if the denominator in simplest form has only 2s and 5s in its prime factorization, the decimal terminates. Any other prime factor (3, 7, 11, 13, ...) forces a repeat. So

\frac{7}{40}

terminates because

40 = 2 \cdot 2 \cdot 2 \cdot 5

, while

\frac{7}{30}

repeats because

30 = 2 \cdot 3 \cdot 5

contains a 3.

Where students go wrong: dividing backwards. For

\frac{3}{8}

, some students divide 8 by 3 and get 2.66, which is bigger than 1 — impossible for a fraction less than 1. Always ask whether your answer is reasonable. A proper fraction must give a decimal between 0 and 1.

Crossing Between Decimals and Percents

Because percent means hundredths, moving between a decimal and a percent is just multiplying or dividing by 100.

Decimal to percent: multiply by 100, which slides the decimal point two places right, then attach the percent symbol. So

0.42 = 42\%

0.7 = 70\%

1.35 = 135\%

, and

0.008 = 0.8\%

.

Percent to decimal: divide by 100, which slides the point two places left, then drop the percent symbol. So

60\% = 0.6

9\% = 0.09

250\% = 2.5

, and

4.5\% = 0.045

.

If you cannot remember which direction, use a number you already know: 50% is one half, and one half is 0.5. Since 50 shrinks to 0.5, percent to decimal must move the point left. Rebuild the rule from that anchor every time instead of guessing.

Decimal	Percent	Check
$0.03$	$3\%$	tiny number, tiny percent
$0.3$	$30\%$	about a third
$3.0$	$300\%$	triple the whole

Two traps show up constantly. First,

0.5\%

is not

0.5

— it is

0.005

, one half of one percent, a very small amount. Second, when a decimal has only one digit, you must write in a placeholder zero:

0.9

becomes

90\%

, not

9\%

. And any percent above 100 must give a decimal greater than 1, which is a fast way to check work involving growth or markups.

Percent to Fraction in Simplest Form

To turn a percent into a fraction, write the number over 100 and simplify by dividing the numerator and denominator by their greatest common factor.

45\% = \frac{45}{100} = \frac{45 \div 5}{100 \div 5} = \frac{9}{20}

If the percent contains a decimal, clear it first by multiplying the top and bottom by the same power of 10. For

12.5\%

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

If the percent contains a fraction, such as

33\frac{1}{3}\%

, write it as

\frac{100/3}{100}

, which equals

\frac{100}{3} \cdot \frac{1}{100} = \frac{1}{3}

. That is why

\frac{1}{3}

is usually reported as about 33.3%, never exactly 33%.

Percents over 100 work the same way and become fractions greater than 1:

160\% = \frac{160}{100} = \frac{8}{5} = 1\frac{3}{5}

.

These conversions are worth memorizing because they appear again in ratios, proportions, and probability:

Fraction	Decimal	Percent
$\frac{1}{2}$	$0.5$	$50\%$
$\frac{1}{3}$	$0.\overline{3}$	$33\frac{1}{3}\%$
$\frac{1}{4}$	$0.25$	$25\%$
$\frac{1}{5}$	$0.2$	$20\%$
$\frac{1}{8}$	$0.125$	$12.5\%$
$\frac{2}{3}$	$0.\overline{6}$	$66\frac{2}{3}\%$

The most common error here is forgetting to simplify.

\frac{45}{100}

is a correct value but not a complete answer when the directions say simplest form.

Using Conversions to Compare and Estimate

Conversions are not busywork — they are how you compare numbers that arrive in different forms. Suppose one class recycled

\frac{7}{8}

of its paper, another recycled 87%, and a third recycled 0.86 of its paper. You cannot rank those until they share a form. Convert everything to decimals:

\frac{7}{8} = 0.875

87\% = 0.87

, and

0.86

stays put. Now the order from greatest to least is clear:

\frac{7}{8}

, then 87%, then 0.86.

Decimals are usually the best common form because comparing place values is fast, as long as you line up the digits and pad with zeros:

0.9

compared with

0.87

becomes

0.90

compared with

0.87

, so

0.9

is larger. Students who compare "9 versus 87" get this backwards.

Repeating decimals need care when you round. Since

\frac{2}{3} = 0.\overline{6}

, rounding to

0.67

is fine for comparing but is not exactly equal, so write

\frac{2}{3} = 0.\overline{6} \approx 0.67

and keep the fraction if you need an exact answer later.

Estimation gives you a safety net. Before dividing, ask what the fraction is close to.

\frac{5}{9}

is a little more than half, so the decimal should be a little more than 0.5 — and indeed

0.\overline{5}

. If your division produced 1.8, you divided in the wrong order. This kind of quick reasonableness check catches most conversion mistakes before they spread into a longer problem.

Key terms

Percent.: A ratio comparing a number to 100; "per hundred." So $37\%$ means $\frac{37}{100}$ or $0.37$ .
Terminating decimal.: A decimal that ends because the division reaches a remainder of 0, such as $\frac{3}{8} = 0.375$ .
Repeating decimal.: A decimal in which one or more digits repeat forever, written with a bar over the repeating digits, such as $\frac{4}{11} = 0.\overline{36}$ .
Bar notation.: The overline used to mark the repeating block of a decimal; in $0.1\overline{6}$ only the 6 repeats.
Rational number.: Any number that can be written as a fraction of two integers with a nonzero denominator. Every rational number has a decimal form that either terminates or repeats.
Simplest form.: A fraction in which the numerator and denominator share no common factor other than 1, reached by dividing both by their greatest common factor.
Place value (decimal).: The position that names a decimal's denominator: $0.7$ is seven tenths, $0.07$ is seven hundredths, $0.007$ is seven thousandths.
Greatest common factor (GCF).: The largest whole number that divides two numbers evenly; used to reduce a percent's fraction form, as when 25 reduces $\frac{75}{100}$ to $\frac{3}{4}$ .

Worked example

Complete every empty cell in this table. Write fractions in simplest form and use bar notation for any repeating decimal.

Fraction	Decimal	Percent
$\frac{5}{8}$	?	?
?	$0.06$	?
?	?	$175\%$
$\frac{5}{6}$	?	?

Row 1, starting from $\frac{5}{8}$ . The fraction bar means divide:

5 \div 8

. Write 5 as

5.000

and divide.

8

into

50

goes 6 times (

48

, remainder 2);

8

into

20

goes 2 times (

16

, remainder 4);

8

into

40

goes 5 times exactly. The decimal is

0.625

, a terminating decimal. Now multiply by 100 to get the percent: the point moves two places right, giving

62.5\%

.

Row 2, starting from $0.06$ . Read the place value: the last digit sits in the hundredths place, so

0.06 = \frac{6}{100}

. The GCF of 6 and 100 is 2, so

\frac{6 \div 2}{100 \div 2} = \frac{3}{50}

. For the percent, move the point two places right:

0.06 = 6\%

. A quick check:

6\%

should be a small slice, and

\frac{3}{50}

is indeed small.

Row 3, starting from $175\%$ . Percent to decimal means divide by 100, so the point moves two places left:

175\% = 1.75

. Because the percent is above 100, the decimal must be above 1 — it is. For the fraction, write it over 100:

\frac{175}{100}

. The GCF of 175 and 100 is 25, so

\frac{175 \div 25}{100 \div 25} = \frac{7}{4}

, which is

1\frac{3}{4}

.

Row 4, starting from $\frac{5}{6}$ . Divide

5 \div 6

6

into

50

goes 8 times (

48

, remainder 2);

6

into

20

goes 3 times (

18

, remainder 2); the remainder 2 repeats forever. So the decimal is

0.8333\ldots = 0.8\overline{3}

, with the bar only over the 3. Since

6 = 2 \cdot 3

contains a factor of 3, a repeat was expected. Multiplying by 100 gives

83.\overline{3}\%

, usually written

83\frac{1}{3}\%

.

Completed table.

Fraction	Decimal	Percent
$\frac{5}{8}$	$0.625$	$62.5\%$
$\frac{3}{50}$	$0.06$	$6\%$
$\frac{7}{4}$	$1.75$	$175\%$
$\frac{5}{6}$	$0.8\overline{3}$	$83\frac{1}{3}\%$

Practice questions

Which decimal is equal to

0.8\%

$0.8$
$0.08$
$0.008$
$8.0$

Answer: $0.008$

Percent to decimal means dividing by 100, so the decimal point slides two places left. Starting at

0.8

and moving left twice gives

0.008

. Reasonableness check:

0.8\%

is less than one percent, so it must be much smaller than

0.01

. The answer

0.8

is what you get by dropping the percent symbol without dividing — that value would actually be

80\%

Write

0.72

as a fraction in simplest form and as a percent.

$\frac{72}{100}$ and $7.2\%$
$\frac{18}{25}$ and $72\%$
$\frac{36}{50}$ and $72\%$
$\frac{18}{25}$ and $0.72\%$

Answer: $\frac{18}{25}$ and $72\%$

The 2 sits in the hundredths place, so

0.72 = \frac{72}{100}

. The GCF of 72 and 100 is 4, giving

\frac{18}{25}

. Stopping at

\frac{72}{100}

\frac{36}{50}

leaves the fraction unsimplified. For the percent, move the point two places right:

72\%

Marcus says that

\frac{4}{9}

and

\frac{4}{25}

should both give terminating decimals because both denominators are perfect squares. Explain whether he is right, convert each fraction to a decimal, and give each as a percent.

Answer: Marcus is wrong. Being a perfect square does not matter; what matters is the prime factorization of the denominator. $25 = 5 \cdot 5$ contains only 5s, so $\frac{4}{25} = 0.16 = 16\%$ terminates. But $9 = 3 \cdot 3$ contains 3s, so $\frac{4}{9} = 0.\overline{4} = 44\frac{4}{9}\%$ repeats.

A decimal terminates only when the simplified denominator's prime factors are all 2s and 5s, because 2 and 5 are the primes that build powers of ten. Dividing

4 \div 25

: you can also scale the fraction, since

\frac{4}{25} = \frac{16}{100} = 0.16

, and moving the point two places right gives

16\%

. Dividing

4 \div 9

keeps returning a remainder of 4, so the digit 4 repeats forever:

0.\overline{4}

. Multiplying by 100 gives

44.\overline{4}\%

, which is exactly

44\frac{4}{9}\%

; rounding to

44.4\%

is an approximation, not an equality.

FAQ

How do I know if a fraction will make a repeating decimal before I divide?: Simplify the fraction, then factor the denominator into primes. If the only primes are 2s and 5s, the decimal terminates. Any other prime factor — 3, 7, 11, 13, and so on — makes it repeat. For example $\frac{9}{40}$ terminates because $40 = 2 \cdot 2 \cdot 2 \cdot 5$ , but $\frac{9}{14}$ repeats because $14 = 2 \cdot 7$ .
Which way does the decimal point move when converting percents?: Percent to decimal moves the point two places left (you divide by 100), and decimal to percent moves it two places right (you multiply by 100). Anchor the rule to a fact you know for sure: 50% is one half, which is 0.5, so 50 must shrink when the percent symbol comes off.
Can a percent be larger than 100 or smaller than 1?: Yes to both. $250\%$ means 2.5 times the whole, which shows up in growth, markups, and comparisons. And $0.4\%$ means four tenths of one percent, or 0.004 as a decimal — useful for very small rates. Only percents describing a part of a single whole are limited to the range from 0 to 100.
Should I round a repeating decimal or keep the fraction?: Keep the fraction whenever you need an exact answer or plan to multiply and divide further, because $0.33$ is not exactly $\frac{1}{3}$ . Round the decimal only for comparing or reporting, and show that it is approximate: $\frac{1}{3} = 0.\overline{3} \approx 0.33$ .

Learn this with a teacher, not a page

The Crimsora tutor teaches Converting Fractions, Decimals & Percents live — explaining on a whiteboard, asking you questions, and adapting to where you get stuck.

Try a live session free