Three typical formats for numbers space fractions, decimals, and percents.

You are watching: 0.6 as a percentage and fraction

Percents are regularly used to connect a family member amount. You have actually probably watched them offered for discounts, where the percent the discount can apply to various prices. Percents are additionally used when stating taxes and also interest prices on savings and loans.


A percent is a ratio of a number to 100. Every cent way “per 100,” or “how many out of 100.” You usage the price % after a number to indicate percent.

Notice that 12 that the 100 squares in the grid below have been shaded green. This to represent 12 percent (12 every 100).


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12% = 12 percent = 12 components out the 100 =

*


How countless of the squares in the grid over are unshaded? since 12 space shaded and also there space a complete of 100 squares, 88 space unshaded. The unshaded section of the whole grid is 88 components out of 100, or 88% the the grid. Notice that the shaded and also unshaded sections together make 100% that the grid (100 the end of 100 squares).


Example

Problem

What percent that the network is shaded?

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The net is split into 100 smaller sized squares, through 10 squares in each row.

23 squares out of 100 squares space shaded.

Answer

23% the the net is shaded.


Example

Problem

What percent of the large square is shaded?

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The grid is divided into 10 rectangles. Because that percents, you need to look at 100 equal-sized parts of the whole. You have the right to divide every of the 10 rectangles into 10 pieces, providing 100 parts.

*

30 small squares out of 100 are shaded.

Answer

30% that the huge square is shaded.


What percent that this network is shaded?

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A) 3%

B) 11%

C) 38%

D) 62%


A) 3%

Incorrect. Three full columns the 10 squares space shaded, plus an additional 8 squares indigenous the next column. So, there are 30 + 8, or 38, squares shaded the end of the 100 squares in the large square. The exactly answer is 38%.

B) 11%

Incorrect. Three full columns of 10 squares room shaded, plus another 8 squares from the following column. So, there space 30 + 8, or 38, squares shaded the end of the 100 squares in the large square. The exactly answer is 38%.

C) 38%

Correct. Three full columns of 10 squares are shaded, plus one more 8 squares from the next column. So, there are 30 + 8, or 38, squares shaded out of the 100 squares in the huge square. This means 38% that the huge square is shaded.

D) 62%

Incorrect. There room 62 tiny unshaded squares out of the 100 in the large square, for this reason the percent of the large square the is unshaded is 62%. However, the question asked what percent is shaded. There room 38 shaded squares the the 100 squares in the large square, therefore the correct answer is 38%.

Rewriting Percents, Decimals, and also Fractions


It is often useful to readjust the layout of a number. Because that example, friend may find it less complicated to include decimals than to include fractions. If you can write the fractions together decimals, you can include them together decimals. Climate you deserve to rewrite your decimal amount as a fraction, if necessary.

Percents deserve to be created as fractions and decimals in very few steps.


Example

Problem

Write 25% as a simplified portion and together a decimal.

Write together a fraction.

25% =

Since % means “out the 100,” 25% way 25 out of 100. You compose this together a fraction, using 100 as the denominator.

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Simplify the fraction by dividing the numerator and denominator by the common factor 25.

Write as a decimal.

25% =  = 0.25

You can additionally just move the decimal allude in the entirety number 25 two areas to the left to acquire 0.25.

Answer

25% =

*
 = 0.25


Notice in the diagram listed below that 25% of a grid is also  of the grid, together you found in the example.

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Notice the in the previous example, rewriting a percent together a decimal takes just a change of the decimal point. You have the right to use fractions to know why this is the case. Any kind of percentage x can be represented as the fraction , and any fraction  can be written as a decimal by moving the decimal allude in x two places to the left. For example, 81% have the right to be composed as

*
, and also dividing 81 by 100 outcomes in 0.81. Civilization often skip over the intermediary fraction step and also just transform a percent come a decimal by moving the decimal suggest two locations to the left.

In the exact same way, rewriting a decimal as a percent (or as a fraction) requires couple of steps.


Example

Problem

Write 0.6 as a percent and also as a simplified fraction.

Write together a percent.

0.6 = 0.60 = 60%

Write 0.6 together 0.60, i beg your pardon is 60 hundredths. 60 hundredths is 60 percent.

You can additionally move the decimal suggest two areas to the appropriate to find the percent equivalent.

Write together a fraction.

0.6 =

*

To compose 0.6 as a fraction, you read the decimal, 6 tenths, and also write 6 one per 10 in fraction form.

*

Simplify the portion by splitting the numerator and denominator by 2, a typical factor.

Answer

0.6 = 60% =

*
 


In this example, the percent is no a whole number. You can handle this in the exact same way, yet it’s usually easier to transform the percent to a decimal and then transform the decimal come a fraction.


Example

Problem

Write 5.6% together a decimal and also as a simplified fraction.

Write together a decimal.

5.6% = 0.056

Move the decimal allude two places to the left. In this case, insert a 0 in former of the 5 (05.6) in order to have the ability to move the decimal come the left two places.

Write together a fraction.

0.056 =

*

Write the fraction as you would read the decimal. The critical digit is in the thousandths place, therefore the denominator is 1,000.

*

Simplify the fraction by separating the numerator and also denominator by 8, a typical factor.

Answer

5.6% =

*
 = 0.056


Write 0.645 as a percent and also as a streamlined fraction.

A) 64.5% and also

B) 0.645% and also

C) 645% and

D) 64.5% and also


Show/Hide Answer

A) 64.5% and also

Correct. 0.645 = 64.5% = .

B) 0.645% and

Incorrect. 0.645 = 64.5%, no 0.645%. Remember that as soon as you transform a decimal to a percent you have to move the decimal allude two places to the right. The correct answer is 64.5% and also .

C) 645% and also

Incorrect. 0.645 = 64.5%, not 645%. Psychic that as soon as you convert a decimal to a percent you need to move the decimal suggest two areas to the right. The exactly answer is 64.5% and also .

D) 64.5% and

Incorrect. To compose 0.645 as a percent, relocate the decimal place two places to the right: 64.5%. To create 0.645 together a fraction, usage 645 together the numerator. The ar value that the critical digit (the 5) is thousandths, so the denominator is 1,000. The portion is . The greatest typical factor of 645 and 1,000 is 5, for this reason you have the right to divide the numerator and also denominator through 5 to obtain . The exactly answer is 64.5% and .

In bespeak to compose a portion as a decimal or a percent, you can write the portion as an equivalent fraction with a denominator the 10 (or any other strength of 10 such as 100 or 1,000), which deserve to be then converted come a decimal and also then a percent.


Example

Problem

Write

*
 as a decimal and also as a percent.

Write together a decimal.

*

Find one equivalent fraction with 10, 100, 1,000, or other power the 10 in the denominator. Due to the fact that 100 is a many of 4, you deserve to multiply 4 through 25 to acquire 100. Main point both the numerator and also the denominator through 25.

 = 0.75

Write the fraction as a decimal with the 5 in the hundredths place.

Write together a percent.

0.75 = 75%

To create the decimal together a percent, relocate the decimal suggest two places to the right.

Answer

*
 = 0.75 = 75%


If that is challenging to find an equivalent fraction with a denominator that 10, 100, 1,000, and so on, you can constantly divide the numerator by the denominator to find the decimal equivalent.


Example

Problem

Write

*
 as a decimal and as a percent.

Write as a decimal.

*

Divide the numerator by the denominator. 3 ÷ 8 = 0.375.

Write together a percent.

0.375 = 37.5%

To write the decimal as a percent, relocate the decimal point two areas to the right.

Answer

*
 = 0.375 = 37.5%


Write  as a decimal and as a percent.

A) 80.0 and also 0.8%

B) 0.4 and also 4%

C) 0.8 and 80%

D) 0.8 and also 8%


Show/Hide Answer

A) 80.0 and 0.8%

Incorrect. Notice that 10 is a lot of of 5, for this reason you have the right to rewrite  using 10 together the denominator. Main point the numerator and also denominator by 2 to acquire . The equivalent decimal is 0.8. You have the right to write this together a percent by relocating the decimal suggest two areas to the right. Since 0.8 has only one place to the right, incorporate 0 in the percentage percent place: 0.8 = 0.80 = 80%. The exactly answer is 0.8 and also 80%.

B) 0.4 and 4%

Incorrect. To uncover a decimal indistinguishable for , very first convert the fraction to tenths. Multiply the numerator and denominator by 2 to gain . The identical decimal is 0.8. So,  and 0.4 space not tantamount quantities. The exactly answer is 0.8 and also 80%.

C) 0.8 and also 80%

Correct. The answer is  = 0.8 = 80%.

D) 0.8 and also 8%

Incorrect. It is true that  = 0.8, yet this does not equal 8%. To write 0.8 together a percent, relocate the decimal point two areas to the right: 0.8 = 0.80 = 80%. The exactly answer is 0.8 and also 80%.

Mixed Numbers


All the previous instances involve fractions and also decimals much less than 1, so every one of the percents you have actually seen so much have been less than 100%.

Percents greater than 100% are possible as well. Percents an ext than 100% are offered to describe cases where there is an ext than one entirety (fractions and decimals better than 1 are used for the exact same reason).

In the diagram below, 115% is shaded. Each grid is considered a whole, and also you need two grids for 115%.

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Expressed as a decimal, the percent 115% is 1.15; together a fraction, that is

*
, or
*
. Notice that you deserve to still convert among percents, fractions, and decimals when the quantity is greater than one whole.

Numbers better than one that encompass a fractional part can be written as the sum of a whole number and the spring part. For instance, the combined number  is the sum of the entirety number 3 and also the portion .  = 3 + .


Example

Problem

Write

*
 as a decimal and also as a percent.

*

Write the mixed portion as 2 wholes plus the spring part.

Write as a decimal.

*

Write the fractional part as a decimal by dividing the numerator by the denominator. 7 ÷ 8 = 0.875.

*

Add 2 come the decimal.

Write together a percent.

2.875 = 287.5%

Now you deserve to move the decimal point two places to the best to compose the decimal as a percent.

Answer

*
 = 2.875 = 287.5%


Note the a totality number have the right to be written as a percent. 100% way one whole; so 2 wholes would be 200%.


Example

Problem

Write 375% together a decimal and as a simplified fraction.

Write together a decimal.

375% = 3.75

Move the decimal allude two places to the left. Keep in mind that there is a totality number along with the decimal together the percent is more than 100%.

Write as a fraction.

3.75 = 3 + 0.75

Write the decimal as a amount of the whole number and the fountain part.

0.75 =

Write the decimal component as a fraction.

*

Simplify the fraction by separating the numerator and denominator by a typical factor the 25.

3 +

*
 =
*

Add the entirety number component to the fraction.

Answer

375% = 3.75=

*


Write 4.12 as a percent and as a streamlined fraction.

A) 0.0412% and also

B) 412% and also

C) 412% and also

D) 4.12% and also


Show/Hide Answer

A) 0.0412% and also

Incorrect. To convert 4.12 come a percent, move the decimal point two locations to the right, no the left. The correct answer is 412% and .

B) 412% and

Correct. 4.12 equals 412%, and the simplified form of  is .

C) 412% and

Incorrect. 4.12 does same 412%, yet it is likewise equivalent come , not

*
. The correct answer is 412% and .

D) 4.12% and

Incorrect. To convert 4.12 come a percent, relocate the decimal suggest two places to the right. The correct answer is 412% and also .

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Summary


Percents space a common way to represent fractional amounts, just as decimals and fractions are. Any number that have the right to be created as a decimal, fraction, or percent can also be written using the other two representations.