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

You are watching: How do you write 0.6 as a fraction

Percents are regularly used to connect a family member amount. You have probably seen them supplied for discounts, where the percent the discount can apply to different prices. Percents are likewise used when stating taxes and also interest rates on savings and also loans.


A percent is a proportion of a number come 100. Every cent way “per 100,” or “how numerous out that 100.” You usage the price % ~ a number to show percent.

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


*

12% = 12 percent = 12 parts out the 100 =

*


How countless of the squares in the grid over are unshaded? due to the fact that 12 space shaded and there room a full of 100 squares, 88 space unshaded. The unshaded section of the totality grid is 88 components out of 100, or 88% of the grid. Notice that the shaded and also unshaded portions together make 100% of the network (100 out of 100 squares).


Example

Problem

What percent of the network is shaded?

*

The net is separated into 100 smaller sized squares, v 10 squares in each row.

23 squares out of 100 squares room shaded.

Answer

23% of the network is shaded.


Example

Problem

What percent of the big square is shaded?

*

The net is divided into 10 rectangles. For percents, you need to look at 100 equal-sized parts of the whole. You can divide each of the 10 rectangles right into 10 pieces, providing 100 parts.

*

30 tiny squares out of 100 space shaded.

Answer

30% of the huge square is shaded.


What percent that this network is shaded?

*

A) 3%

B) 11%

C) 38%

D) 62%


A) 3%

Incorrect. Three complete columns that 10 squares space shaded, plus an additional 8 squares indigenous the next 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%.

B) 11%

Incorrect. Three complete columns of 10 squares room 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 big square. The correct answer is 38%.

C) 38%

Correct. Three complete columns that 10 squares room shaded, plus an additional 8 squares from the next column. So, there space 30 + 8, or 38, squares shaded the end of the 100 squares in the large 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, therefore the percent of the large square the is unshaded is 62%. However, the inquiry asked what percent is shaded. There room 38 shaded squares that the 100 squares in the huge square, therefore the exactly answer is 38%.

Rewriting Percents, Decimals, and also Fractions


It is often helpful to readjust the layout of a number. Because that example, girlfriend may find it less complicated to add decimals 보다 to include fractions. If you have the right to write the fractions together decimals, girlfriend can add them as decimals. Then you can rewrite your decimal amount as a fraction, if necessary.

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


Example

Problem

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

Write together a fraction.

25% =

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

*

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

Write together a decimal.

25% =  = 0.25

You can also just move the decimal suggest in the whole number 25 two locations to the left to acquire 0.25.

Answer

25% =

*
 = 0.25


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

*

Notice that in the vault example, rewriting a percent together a decimal takes just a shift of the decimal point. You have the right to use fractions to recognize why this is the case. Any type of percentage x can be represented as the portion , and any fraction  can be created as a decimal by moving the decimal suggest in x two places to the left. For example, 81% can be composed as

*
, and dividing 81 by 100 results in 0.81. People often skip end the intermediary portion step and just convert a percent come a decimal by relocating the decimal suggest two places to the left.

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


Example

Problem

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

Write as a percent.

0.6 = 0.60 = 60%

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

You can additionally move the decimal point two places to the appropriate to discover the percent equivalent.

Write as a fraction.

0.6 =

*

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

*

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

Answer

0.6 = 60% =

*
 


In this example, the percent is not a entirety number. You can handle this in the exact same way, yet it’s usually less complicated to convert the percent come a decimal and also then transform the decimal to a fraction.


Example

Problem

Write 5.6% as 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 bespeak to be able to move the decimal come the left two places.

Write as a fraction.

0.056 =

*

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

*

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

Answer

5.6% =

*
 = 0.056


Write 0.645 together a percent and as a simplified fraction.

A) 64.5% and

B) 0.645% and also

C) 645% and also

D) 64.5% and also


Show/Hide Answer

A) 64.5% and

Correct. 0.645 = 64.5% = .

B) 0.645% and also

Incorrect. 0.645 = 64.5%, not 0.645%. Psychic that when you convert a decimal to a percent you have to move the decimal suggest two locations to the right. The correct answer is 64.5% and .

C) 645% and

Incorrect. 0.645 = 64.5%, not 645%. Remember that when you convert a decimal to a percent you need to move the decimal point two areas to the right. The correct answer is 64.5% and .

D) 64.5% and also

Incorrect. To create 0.645 as a percent, move the decimal ar two locations to the right: 64.5%. To create 0.645 together a fraction, usage 645 as the numerator. The place 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, therefore you deserve to divide the numerator and denominator by 5 to gain . The exactly answer is 64.5% and also .

In stimulate to create a portion as a decimal or a percent, you have the right to write the fraction as an equivalent fraction with a denominator that 10 (or any kind 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 as a percent.

Write together a decimal.

*

Find one equivalent portion with 10, 100, 1,000, or various other power that 10 in the denominator. Due to the fact that 100 is a lot of of 4, you deserve to multiply 4 through 25 to obtain 100. Multiply both the numerator and also the denominator by 25.

 = 0.75

Write the fraction as a decimal through the 5 in the percentage percent place.

Write as a percent.

0.75 = 75%

To create the decimal together a percent, move the decimal suggest two locations to the right.

Answer

*
 = 0.75 = 75%


If that is complicated to find an equivalent portion with a denominator of 10, 100, 1,000, and so on, friend can constantly divide the molecule by the denominator to discover 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 as a percent.

0.375 = 37.5%

To create the decimal together a percent, relocate the decimal allude 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 4%

C) 0.8 and also 80%

D) 0.8 and also 8%


Show/Hide Answer

A) 80.0 and also 0.8%

Incorrect. An alert that 10 is a multiple of 5, so you have the right to rewrite  using 10 together the denominator. Main point the numerator and also denominator by 2 to gain . The indistinguishable decimal is 0.8. You deserve to write this together a percent by moving the decimal suggest two places 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 correct answer is 0.8 and also 80%.

B) 0.4 and also 4%

Incorrect. To uncover a decimal indistinguishable for , an initial convert the portion to tenths. Multiply the numerator and denominator by 2 to acquire . The tantamount decimal is 0.8. So,  and 0.4 space not indistinguishable quantities. The correct answer is 0.8 and 80%.

C) 0.8 and also 80%

Correct. The price is  = 0.8 = 80%.

D) 0.8 and also 8%

Incorrect. It is true the  = 0.8, however this does not equal 8%. To create 0.8 as a percent, relocate the decimal allude two locations to the right: 0.8 = 0.80 = 80%. The correct answer is 0.8 and also 80%.

Mixed Numbers


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

Percents greater than 100% are feasible as well. Percents more than 100% are used to describe instances where there is more than one entirety (fractions and decimals higher than 1 are offered for the same reason).

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

*

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

*
, or
*
. Notice that you deserve to still convert amongst percents, fractions, and also decimals once the quantity is higher than one whole.

Numbers better than one that incorporate a fractional component can be composed as the sum of a totality number and also the fractional part. For instance, the mixed number  is the amount of the entirety number 3 and the portion .  = 3 + .


Example

Problem

Write

*
 as a decimal and as a percent.

*

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

Write together a decimal.

*

Write the fractional component as a decimal by splitting the numerator 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 right to create the decimal as a percent.

Answer

*
 = 2.875 = 287.5%


Note that a totality number can be created as a percent. 100% means one whole; so 2 wholes would certainly 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 allude two areas to the left. Keep in mind that over there is a entirety 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 fractional part.

0.75 =

Write the decimal part as a fraction.

*

Simplify the portion by splitting the numerator and also denominator by a usual factor that 25.

3 +

*
 =
*

Add the totality number component to the fraction.

Answer

375% = 3.75=

*


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

A) 0.0412% and

B) 412% and also

C) 412% and also

D) 4.12% and also


Show/Hide Answer

A) 0.0412% and

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

B) 412% and also

Correct. 4.12 amounts to 412%, and also the simplified kind of  is .

C) 412% and

Incorrect. 4.12 does equal 412%, yet it is also equivalent to , no

*
. The correct answer is 412% and also .

D) 4.12% and also

Incorrect. To transform 4.12 come a percent, relocate the decimal allude two places to the right. The exactly answer is 412% and .

See more: How To Build An Indoor Pitching Mound Plans: Step By Step Instructions


Summary


Percents space a common means to stand for fractional amounts, simply as decimals and fractions are. Any number that deserve to be composed as a decimal, fraction, or percent can also be written utilizing the various other two representations.