Three common formats because that numbers room fractions, decimals, and percents.

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Percents are frequently used to interact a family member amount. You have probably watched them provided for discounts, whereby the percent the discount can apply to different prices. Percents are also used when discussing taxes and interest prices on savings and loans.


A percent is a ratio of a number come 100. Per cent way “per 100,” or “how plenty of out of 100.” You usage the price % after ~ a number to show percent.

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


*

12% = 12 percent = 12 components out that 100 =

*


How many of the squares in the grid above are unshaded? because 12 space shaded and also there space a complete of 100 squares, 88 are unshaded. The unshaded section of the totality grid is 88 components out of 100, or 88% that the grid. Notification that the shaded and unshaded sections together make 100% the the grid (100 the end of 100 squares).


Example

Problem

What percent the the grid is shaded?

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

23 squares the end of 100 squares are shaded.

Answer

23% that the network is shaded.


Example

Problem

What percent of the huge square is shaded?

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The network is split into 10 rectangles. Because that percents, you must look in ~ 100 equal-sized components of the whole. You deserve to divide each of the 10 rectangles right into 10 pieces, offering 100 parts.

*

30 small squares out of 100 room shaded.

Answer

30% of the large square is shaded.


What percent of this network is shaded?

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A) 3%

B) 11%

C) 38%

D) 62%


A) 3%

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

B) 11%

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

C) 38%

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

D) 62%

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

Rewriting Percents, Decimals, and also Fractions


It is often advantageous to change the style of a number. For example, girlfriend may find it simpler to add decimals 보다 to add fractions. If you deserve to write the fractions together decimals, you can add them as decimals. Climate you deserve to rewrite your decimal amount as a fraction, if necessary.

Percents deserve to be written as fractions and 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 of 100,” 25% way 25 out of 100. You write this as a fraction, making use of 100 as the denominator.

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Simplify the fraction by splitting the numerator and also denominator by the usual factor 25.

Write together a decimal.

25% =  = 0.25

You can likewise just move the decimal allude in the whole number 25 two places to the left to acquire 0.25.

Answer

25% =

*
 = 0.25


Notice in the diagram listed below that 25% of a network is likewise  of the grid, together you uncovered in the example.

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Notice the in the previous example, rewriting a percent together a decimal takes simply a shift of the decimal point. You deserve to use fountain to recognize why this is the case. Any percentage x deserve to be represented as the fraction , and also any fraction  can be created as a decimal by relocating the decimal suggest in x two locations to the left. For example, 81% deserve to be written as

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

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


Example

Problem

Write 0.6 together a percent and as a simplified fraction.

Write together a percent.

0.6 = 0.60 = 60%

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

You can also move the decimal suggest two locations to the appropriate to find the percent equivalent.

Write as a fraction.

0.6 =

*

To compose 0.6 together a fraction, you review the decimal, 6 tenths, and write 6 tenths in portion form.

*

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

Answer

0.6 = 60% =

*
 


In this example, the percent is no a entirety number. You can handle this in the same way, but it’s usually much easier to convert the percent to a decimal and also then convert the decimal come a fraction.


Example

Problem

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

Write as a decimal.

5.6% = 0.056

Move the decimal point two locations to the left. In this case, insert a 0 in front of the 5 (05.6) in stimulate to have the ability to move the decimal to the left 2 places.

Write as a fraction.

0.056 =

*

Write the portion as girlfriend would review the decimal. The critical digit is in the thousandths place, therefore the denominator is 1,000.

*

Simplify the portion by dividing the numerator and denominator by 8, a usual 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

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%. Mental that when 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 also .

C) 645% and also

Incorrect. 0.645 = 64.5%, no 645%. Remember that as soon as you convert a decimal come a percent you have to move the decimal point two areas to the right. The exactly answer is 64.5% and .

D) 64.5% and also

Incorrect. To create 0.645 together a percent, move the decimal ar two locations to the right: 64.5%. To create 0.645 as a fraction, use 645 together the numerator. The location value the the last digit (the 5) is thousandths, therefore the denominator is 1,000. The portion is . The greatest common factor of 645 and 1,000 is 5, therefore you have the right to divide the numerator and also denominator by 5 to obtain . The exactly answer is 64.5% and also .

In order to write a portion as a decimal or a percent, you can write the fraction as an equivalent portion with a denominator that 10 (or any other power of 10 such together 100 or 1,000), which have the right 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 an equivalent portion with 10, 100, 1,000, or various other power the 10 in the denominator. Since 100 is a multiple of 4, you have the right to multiply 4 by 25 to gain 100. Multiply both the numerator and the denominator through 25.

 = 0.75

Write the portion 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 locations to the right.

Answer

*
 = 0.75 = 75%


If the is an overwhelming to uncover an equivalent portion with a denominator the 10, 100, 1,000, and so on, friend can constantly divide the molecule by the denominator to find 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 create the decimal together a percent, move 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 4%

C) 0.8 and 80%

D) 0.8 and also 8%


Show/Hide Answer

A) 80.0 and 0.8%

Incorrect. An alert that 10 is a lot of of 5, for this reason you can rewrite  using 10 together the denominator. Multiply the numerator and denominator by 2 to gain . The equivalent decimal is 0.8. You have the right to write this as a percent by moving the decimal point two areas to the right. Since 0.8 has only one location to the right, encompass 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 find a decimal identical for , first convert the fraction to tenths. Main point the numerator and denominator by 2 to gain . The equivalent decimal is 0.8. So,  and 0.4 are not equivalent 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 8%

Incorrect. That is true that  = 0.8, yet this does no equal 8%. To write 0.8 as a percent, move the decimal allude two places to the right: 0.8 = 0.80 = 80%. The exactly answer is 0.8 and 80%.

Mixed Numbers


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

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

In the diagram below, 115% is shaded. Every grid is taken into consideration a whole, and you require two grids for 115%.

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

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

Numbers better than one that include a fractional component can be composed as the sum of a whole number and also the fountain part. For instance, the mixed number  is the sum of the entirety number 3 and the fraction .  = 3 + .


Example

Problem

Write

*
 as a decimal and as a percent.

*

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

Write together a decimal.

*

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

*

Add 2 come the decimal.

Write together a percent.

2.875 = 287.5%

Now you can move the decimal allude two areas to the ideal to compose the decimal as a percent.

Answer

*
 = 2.875 = 287.5%


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


Example

Problem

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

Write together a decimal.

375% = 3.75

Move the decimal suggest two locations to the left. Keep in mind that there is a whole number along with the decimal together the percent is much more than 100%.

Write together a fraction.

3.75 = 3 + 0.75

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

0.75 =

Write the decimal part as a fraction.

*

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

3 +

*
 =
*

Add the whole number part to the fraction.

Answer

375% = 3.75=

*


Write 4.12 together a percent and as a streamlined fraction.

A) 0.0412% and

B) 412% and

C) 412% and also

D) 4.12% and


Show/Hide Answer

A) 0.0412% and

Incorrect. To transform 4.12 come a percent, relocate the decimal allude two places to the right, not the left. The exactly answer is 412% and .

B) 412% and also

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

C) 412% and

Incorrect. 4.12 does equal 412%, yet it is additionally equivalent come , not

*
. The exactly answer is 412% and also .

D) 4.12% and

Incorrect. To transform 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 method to represent fractional amounts, simply as decimals and also fractions are. Any type of number that deserve to be composed as a decimal, fraction, or percent can additionally be written making use of the other two representations.