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

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Percents are regularly used to connect a relative amount. You have probably checked out them supplied for discounts, whereby the percent of discount can apply to various prices. Percents are also used when pointing out taxes and interest rates on savings and loans.


A percent is a ratio of a number come 100. Per cent method “per 100,” or “how countless out that 100.” You use the prize % after a number to indicate percent.

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


*

12% = 12 percent = 12 components out of 100 =

*


How plenty of of the squares in the grid over are unshaded? since 12 room shaded and also there room a complete of 100 squares, 88 room unshaded. The unshaded part of the entirety grid is 88 parts out the 100, or 88% the the grid. Notification that the shaded and unshaded portions together do 100% that the network (100 the end of 100 squares).


Example

Problem

What percent of the net is shaded?

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The grid is divided into 100 smaller squares, v 10 squares in every row.

23 squares the end of 100 squares room shaded.

Answer

23% of the grid is shaded.


Example

Problem

What percent of the huge square is shaded?

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The grid is divided into 10 rectangles. Because that percents, you must look in ~ 100 equal-sized components of the whole. You have the right to divide every of the 10 rectangles right into 10 pieces, offering 100 parts.

*

30 tiny squares out of 100 are shaded.

Answer

30% the the large square is shaded.


What percent the 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 are shaded, plus an additional 8 squares native the following column. So, there space 30 + 8, or 38, squares shaded the end of the 100 squares in the large square. The correct answer is 38%.

B) 11%

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

C) 38%

Correct. Three full columns that 10 squares room shaded, plus another 8 squares indigenous the next column. So, there space 30 + 8, or 38, squares shaded the end of the 100 squares in the huge square. This method 38% the the big square is shaded.

D) 62%

Incorrect. There are 62 little unshaded squares the end of the 100 in the huge square, therefore the percent the the big square that is unshaded is 62%. However, the concern asked what percent is shaded. There room 38 shaded squares of the 100 squares in the large square, for this reason the exactly answer is 38%.

Rewriting Percents, Decimals, and Fractions


It is often advantageous to readjust the format of a number. For example, girlfriend may uncover it easier to include decimals than to add fractions. If you have the right to write the fractions together decimals, girlfriend can include them as decimals. Climate you deserve to rewrite your decimal amount as a fraction, if necessary.

Percents have the right to be composed as fractions and decimals in very couple of steps.


Example

Problem

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

Write together a fraction.

25% =

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

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

Write as a decimal.

25% =  = 0.25

You can also just relocate the decimal allude in the entirety number 25 two locations to the left to get 0.25.

Answer

25% =

*
 = 0.25


Notice in the diagram listed below that 25% that a network is additionally  of the grid, as you discovered in the example.

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Notice the in the ahead example, rewriting a percent together a decimal takes simply a transition of the decimal point. You have the right to use fractions to know why this is the case. Any kind of percentage x deserve to be stood for as the fraction , and also any fraction  can be created as a decimal by moving the decimal suggest in x two areas to the left. Because that example, 81% have the right to be composed as

*
, and also dividing 81 through 100 results in 0.81. People often skip end the intermediary fraction step and just transform a percent come a decimal by relocating the decimal suggest two areas to the left.

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


Example

Problem

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

Write together a percent.

0.6 = 0.60 = 60%

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

You can likewise move the decimal point two places to the ideal to discover the percent equivalent.

Write as a fraction.

0.6 =

*

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

*

Simplify the fraction by dividing the numerator and also denominator by 2, a usual factor.

Answer

0.6 = 60% =

*
 


In this example, the percent is not a whole number. You can handle this in the exact same way, but it’s usually easier to convert the percent to a decimal and also then convert the decimal come a fraction.


Example

Problem

Write 5.6% as a decimal and as a streamlined fraction.

Write together a decimal.

5.6% = 0.056

Move the decimal point two places to the left. In this case, insert a 0 in front of the 5 (05.6) in order to be able to move the decimal come the left two places.

Write together a fraction.

0.056 =

*

Write the portion as friend would check out the decimal. The last digit is in the thousandths place, for this reason the denominator is 1,000.

*

Simplify the fraction by dividing the numerator and denominator through 8, a typical factor.

Answer

5.6% =

*
 = 0.056


Write 0.645 together a percent and as a simplified fraction.

A) 64.5% and also

B) 0.645% and

C) 645% and also

D) 64.5% and


Show/Hide Answer

A) 64.5% and also

Correct. 0.645 = 64.5% = .

B) 0.645% and also

Incorrect. 0.645 = 64.5%, no 0.645%. Psychic that once you transform a decimal to a percent you have to move the decimal point two areas to the right. The exactly answer is 64.5% and .

C) 645% and

Incorrect. 0.645 = 64.5%, no 645%. Mental that when you transform a decimal to a percent you have to move the decimal point two places to the right. The correct answer is 64.5% and .

D) 64.5% and also

Incorrect. To write 0.645 together a percent, move the decimal location two places to the right: 64.5%. To compose 0.645 together a fraction, usage 645 as the numerator. The location value that the critical digit (the 5) is thousandths, for this reason the denominator is 1,000. The fraction is . The greatest common factor the 645 and also 1,000 is 5, so you can divide the numerator and also denominator by 5 to obtain . The exactly answer is 64.5% and also .

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


Example

Problem

Write

*
 as a decimal and also as a percent.

Write as a decimal.

*

Find an equivalent portion with 10, 100, 1,000, or other power the 10 in the denominator. Since 100 is a lot of of 4, you can multiply 4 by 25 to obtain 100. Main point both the numerator and the denominator by 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 as a percent, relocate the decimal point two places to the right.

Answer

*
 = 0.75 = 75%


If it is difficult to uncover an equivalent fraction with a denominator the 10, 100, 1,000, and also so on, you can always divide the molecule by the denominator to uncover the decimal equivalent.


Example

Problem

Write

*
 as a decimal and also as a percent.

Write as a decimal.

*

Divide the molecule 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 suggest 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 4%

C) 0.8 and 80%

D) 0.8 and 8%


Show/Hide Answer

A) 80.0 and also 0.8%

Incorrect. Notice that 10 is a lot of of 5, therefore you have the right to rewrite  using 10 as the denominator. Main point the numerator and denominator through 2 to obtain . The equivalent decimal is 0.8. You have the right to write this together a percent by relocating the decimal allude two places to the right. Due to the fact that 0.8 has only one place to the right, include 0 in the hundredths place: 0.8 = 0.80 = 80%. The correct answer is 0.8 and also 80%.

B) 0.4 and also 4%

Incorrect. To find a decimal indistinguishable for , first convert the fraction to tenths. Main point the numerator and also denominator by 2 to get . The equivalent decimal is 0.8. So,  and 0.4 room not tantamount quantities. The correct answer is 0.8 and 80%.

C) 0.8 and also 80%

Correct. The prize is  = 0.8 = 80%.

D) 0.8 and also 8%

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

Mixed Numbers


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

Percents better than 100% are possible as well. Percents much more than 100% are provided to describe cases where over there is much more than one totality (fractions and decimals higher than 1 are provided for the very same reason).

In the chart below, 115% is shaded. Every grid is considered a whole, and also you need two grids because that 115%.

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

*
, or
*
. An alert that you deserve to still convert amongst percents, fractions, and decimals when the quantity is higher than one whole.

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


Example

Problem

Write

*
 as a decimal and also as a percent.

*

Write the mixed fraction as 2 wholes add to the spring part.

Write as a decimal.

*

Write the fractional component as a decimal by separating the molecule by the denominator. 7 ÷ 8 = 0.875.

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Add 2 come the decimal.

Write together a percent.

2.875 = 287.5%

Now you deserve to move the decimal allude two areas to the ideal to compose the decimal together a percent.

Answer

*
 = 2.875 = 287.5%


Note that a whole number can be created as a percent. 100% way one whole; so two wholes would certainly be 200%.


Example

Problem

Write 375% together a decimal and also as a streamlined fraction.

Write as a decimal.

375% = 3.75

Move the decimal allude two places to the left. Note that over there is a totality number together 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 totality number and also the spring part.

0.75 =

Write the decimal part as a fraction.

*

Simplify the portion by separating the numerator and denominator through a usual factor the 25.

3 +

*
 =
*

Add the whole number part to the fraction.

Answer

375% = 3.75=

*


Write 4.12 as a percent and also as a simplified fraction.

A) 0.0412% and also

B) 412% and

C) 412% and also

D) 4.12% and also


Show/Hide Answer

A) 0.0412% and also

Incorrect. To convert 4.12 to a percent, move the decimal point two places to the right, not the left. The correct answer is 412% and .

B) 412% and also

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

C) 412% and

Incorrect. 4.12 does equal 412%, yet it is likewise equivalent to , not

*
. The exactly answer is 412% and also .

D) 4.12% and also

Incorrect. To convert 4.12 come a percent, move the decimal point two places to the right. The exactly answer is 412% and also .

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Summary


Percents room a common method to stand for fractional amounts, just as decimals and fractions are. Any kind of number that can be composed as a decimal, fraction, or percent can likewise be written using the various other two representations.