Three usual formats for numbers are fractions, decimals, and also percents.

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Percents are frequently used to connect a loved one amount. You have actually probably viewed them supplied for discounts, where the percent the discount can use to different prices. Percents are additionally used when pointing out taxes and also interest rates on savings and loans.


A percent is a ratio of a number to 100. Every cent means “per 100,” or “how countless out of 100.” You use the price % ~ a number to indicate percent.

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


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12% = 12 percent = 12 parts out of 100 =

*


How numerous of the squares in the grid over are unshaded? since 12 are shaded and also there are a complete of 100 squares, 88 room unshaded. The unshaded portion of the whole grid is 88 components out of 100, or 88% of the grid. An alert that the shaded and also unshaded parts together make 100% that the net (100 the end of 100 squares).


Example

Problem

What percent that the grid is shaded?

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The network is divided into 100 smaller sized squares, through 10 squares in each row.

23 squares out of 100 squares space shaded.

Answer

23% of the network is shaded.


Example

Problem

What percent the the big square is shaded?

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The net is split into 10 rectangles. For percents, you have to look in ~ 100 equal-sized components of the whole. You have the right to divide each of the 10 rectangles into 10 pieces, giving 100 parts.

*

30 little squares out of 100 are shaded.

Answer

30% of the big square is shaded.


What percent the this grid is shaded?

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A) 3%

B) 11%

C) 38%

D) 62%


A) 3%

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

B) 11%

Incorrect. Three complete columns the 10 squares space shaded, plus another 8 squares from the next column. So, there are 30 + 8, or 38, squares shaded the end of the 100 squares in the huge square. The correct answer is 38%.

C) 38%

Correct. Three complete columns of 10 squares are shaded, plus one more 8 squares indigenous the next column. So, there room 30 + 8, or 38, squares shaded out of the 100 squares in the huge square. This method 38% of the huge square is shaded.

D) 62%

Incorrect. There space 62 little unshaded squares the end of the 100 in the big square, therefore the percent the the big square that is unshaded is 62%. However, the question asked what percent is shaded. There space 38 shaded squares the the 100 squares in the big square, so the exactly answer is 38%.

Rewriting Percents, Decimals, and Fractions


It is often helpful to change the format of a number. For example, you may discover it much easier to add decimals 보다 to add fractions. If you deserve to write the fractions as decimals, girlfriend can include them as decimals. Climate you have the right to rewrite your decimal amount as a fraction, if necessary.

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


Example

Problem

Write 25% together a simplified fraction and together a decimal.

Write as a fraction.

25% =

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

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Simplify the fraction by splitting the numerator and denominator through the typical factor 25.

Write together a decimal.

25% =  = 0.25

You can likewise just relocate the decimal point in the totality number 25 two locations to the left to obtain 0.25.

Answer

25% =

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 = 0.25


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

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

*
, and also dividing 81 by 100 outcomes in 0.81. Human being often skip end the intermediary portion step and also just transform a percent to a decimal by moving the decimal allude two locations to the left.

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


Example

Problem

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

Write as a percent.

0.6 = 0.60 = 60%

Write 0.6 together 0.60, which is 60 hundredths. 60 hundredths is 60 percent.

You can additionally move the decimal suggest two places to the right to uncover the percent equivalent.

Write together a fraction.

0.6 =

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To write 0.6 together a fraction, you review the decimal, 6 tenths, and write 6 one per 10 in fraction form.

*

Simplify the portion by separating the numerator and also denominator by 2, a usual factor.

Answer

0.6 = 60% =

*
 


In this example, the percent is not a totality number. You deserve to handle this in the same way, yet it’s usually easier to transform the percent come a decimal and also then transform the decimal to a fraction.


Example

Problem

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

Write as a decimal.

5.6% = 0.056

Move the decimal allude two areas 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 2 places.

Write as a fraction.

0.056 =

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Write the fraction as girlfriend would review the decimal. The last digit is in the thousandths place, so the denominator is 1,000.

*

Simplify the portion by separating the numerator and also denominator by 8, a common factor.

Answer

5.6% =

*
 = 0.056


Write 0.645 together a percent and as a streamlined fraction.

A) 64.5% and

B) 0.645% and also

C) 645% and

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%, not 0.645%. Remember that as soon as you transform a decimal to a percent you need to move the decimal suggest two areas to the right. The correct answer is 64.5% and .

C) 645% and

Incorrect. 0.645 = 64.5%, not 645%. Psychic that when you transform a decimal to a percent you need to move the decimal allude two locations to the right. The correct answer is 64.5% and .

D) 64.5% and also

Incorrect. To compose 0.645 together a percent, relocate the decimal ar two areas to the right: 64.5%. To compose 0.645 together a fraction, usage 645 as the numerator. The place value of the last digit (the 5) is thousandths, therefore the denominator is 1,000. The fraction is . The greatest common factor of 645 and 1,000 is 5, for this reason you deserve to divide the numerator and denominator by 5 to gain . The exactly answer is 64.5% and also .

In bespeak to create a fraction as a decimal or a percent, you can write the portion as an equivalent portion with a denominator of 10 (or any kind of other strength of 10 such together 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. Since 100 is a lot of of 4, you have the right to multiply 4 by 25 to obtain 100. Main point both the numerator and the denominator through 25.

 = 0.75

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

Write as a percent.

0.75 = 75%

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

Answer

*
 = 0.75 = 75%


If that is complicated to find an equivalent portion with a denominator the 10, 100, 1,000, and so on, you can always divide the molecule by the denominator to discover the decimal equivalent.


Example

Problem

Write

*
 as a decimal and also as a percent.

Write together a decimal.

*

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

Write as a percent.

0.375 = 37.5%

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

Answer

*
 = 0.375 = 37.5%


Write  as a decimal and also as a percent.

A) 80.0 and 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 also 0.8%

Incorrect. Notice that 10 is a lot of of 5, so you deserve to rewrite  using 10 together the denominator. Main point the numerator and denominator by 2 to gain . The tantamount decimal is 0.8. You deserve to write this as a percent by moving the decimal suggest two areas to the right. Because 0.8 has actually only one location to the right, include 0 in the percentage percent place: 0.8 = 0.80 = 80%. The exactly answer is 0.8 and 80%.

B) 0.4 and 4%

Incorrect. To discover a decimal tantamount for , very first convert the portion to tenths. Main point the numerator and denominator by 2 to gain . The identical decimal is 0.8. So,  and 0.4 space not identical quantities. The correct answer is 0.8 and also 80%.

C) 0.8 and also 80%

Correct. The prize is  = 0.8 = 80%.

D) 0.8 and also 8%

Incorrect. That is true the  = 0.8, but this does no equal 8%. To compose 0.8 as a percent, move the decimal point 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 decimals less than 1, so all of the percents you have actually seen so far have been less than 100%.

Percents greater than 100% are possible as well. Percents more than 100% are supplied to describe situations where over there is much more than one totality (fractions and also decimals better than 1 are used for the very same reason).

In the chart below, 115% is shaded. Each grid is thought about 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; as a fraction, it is

*
, or
*
. An alert that you have the right to still convert among percents, fractions, and decimals as soon as the quantity is greater 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 fountain part. For instance, the combined number  is the amount of the whole number 3 and also the portion .  = 3 + .


Example

Problem

Write

*
 as a decimal and also as a percent.

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Write the mixed portion as 2 wholes add to 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.

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Add 2 to the decimal.

Write together a percent.

2.875 = 287.5%

Now you can move the decimal allude two places to the appropriate to compose the decimal together a percent.

Answer

*
 = 2.875 = 287.5%


Note the a totality number deserve to be composed as a percent. 100% way one whole; so 2 wholes would certainly be 200%.


Example

Problem

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

Write together a decimal.

375% = 3.75

Move the decimal suggest two places to the left. Keep in mind that over there is a entirety number along with the decimal as the percent is an ext than 100%.

Write as a fraction.

3.75 = 3 + 0.75

Write the decimal together a sum of the totality number and the spring part.

0.75 =

Write the decimal part as a fraction.

*

Simplify the fraction by splitting the numerator and also denominator through a typical factor that 25.

3 +

*
 =
*

Add the whole number component to the fraction.

Answer

375% = 3.75=

*


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

A) 0.0412% and also

B) 412% and also

C) 412% and

D) 4.12% and


Show/Hide Answer

A) 0.0412% and

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

B) 412% and also

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

C) 412% and also

Incorrect. 4.12 does equal 412%, however it is also equivalent come , not

*
. The correct answer is 412% and also .

D) 4.12% and also

Incorrect. To convert 4.12 to a percent, move the decimal suggest two locations to the right. The correct answer is 412% and .

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Summary


Percents room a common means to represent fractional amounts, simply as decimals and fractions are. Any type of number that can be composed as a decimal, fraction, or percent can also be written utilizing the other two representations.