Decimals to Fractions, and Percentages too: Do the Math or Use a Chart

decimal in c#Decimals, fractions, and percentages are three different ways of showing the same value. Each one is used in mathematics and in science. Engineering, business, and designing firms need to speak in certain mathematical terms to do their work. Figures don’t always come to you in the way you need them. Being able to convert between decimals, fractions, and percent is helpful in all of these areas. Want to learn more about math for business? Take a course at Udemy.

Converting from a Percent to a Decimal

First, we’ll discuss how to convert from a percent to a decimal, because it is rather easy.

Take 25%, we know that 25% is 0.25 (and also 1/4), but how do we arrive at the 0.25?

Use this simple trick:

Think of 25% as 25. of a percent now move that decimal two places to the left and you have 0.25.

You always move two places to convert from percent to decimal. A trick to help you is this: alphabetically, Decimal comes before Percent. So you move left to convert to decimal, right to convert to a percent.

Let’s try it the other way:

0.76=76.0= 76%

Converting from a Decimal to a Fraction

Now converting from a decimal to a fraction is a bit more challenging depending on the figures. It might be simply putting the percentage over the place that the last digit in your decimal is.

Take 0.76, there are two digits in this number. The last digit is in the hundredth place. There is not much to do except to put the 76 over the 100 in a fraction:

0.76=76/100

Now we need to reduce this fraction to its lowest terms. We can do this by dividing both the numerator and denominator by 4, because 4 is the greatest common factor of both the numbers 76 and 100.

76/100=

76/4=19

100/4=25

76/100=19/25

Converting from a decimal to a fraction using Algebra

There are some conversions which require a bit of algebra to convert. If you haven’t done algebra in many years, this can be daunting. (Learn Beginning Algebra at Udemy.com.) For instance:

To convert 0.33 to a fraction,

Notice that the number has the repeating digit 3.

Move the decimal point in this number to the right 1 place (the same number of digits in the number 3).

We get 3.300000

Now we have two numbers with the same repeating decimal parts, 3.300000 and 0.330000.

It will take a bit of algebra to finish the conversion. Your original number will be x. So, x=0.330000. The number with the decimal point slid over can be called 10x, because 10x=3.300000

Now subtract these two equations (subtract the items on the left of the equal sign from those on the right of the equal sign).

10x = 3.3

– x = 0.33

———

9x = 2.97

Notice how all of the repeating decimal parts have been subtracted away We now have 3 simple non-repeating digits on the right side of the equal sign.

Solving 9x=3 for x by dividing both sides of it by 9, we get your answer x=3/9.

Confused?  Remember above, x was originally set equal to 0.330000 via x=0.330000, and now we have that x is also equal to 3/9, so that means 0.330000=3/9.

Now we can reduce this fraction to lowest terms by dividing both the numerator and denominator by 3 (the greatest common factor).

0.33=1/3

Stumped? Udemy.com can help you learn math.

Decimal to Fraction Chart

A decimal to fraction chart is a table of commonly used decimals and their fraction equivalents. These charts can be very helpful and time-saving in business, science, and engineering fields.

You can find them online with percentages, reduced fractions, mm, etc. Some charts are specifically for engineering, some are for the sizes of screws and nails for contractors, and others are for chemistry lab use which would be used in pharmaceutical and food labs.

Here is a basic conversion chart I have compiled:

The decimals and percentages are not accurate; they have been rounded.

FractionDecimalPercent
1/20.550%
1/30.33333.333%
2/30.66666.666%
1/40.2525%
3/40.7575%
1/50.220%
2/50.440%
3/50.660%
4/50.880%
1/60.166616.666%
5/60.833383.333%
1/80.12512.5%
3/80.37537.5%
5/80.62562.5%
7/80.87587.5%
1/90.11111.111%
2/90.22222.222%
4/90.44444.444%
5/90.55555.555%
7/90.77777.777%
8/90.88888.888%
1/100.110%
1/120.083338.333%
1/160.06256.25%
1/320.031253.125%

 

Online Resources

Some other resources can be found online, here are a few helpful ones I found:

Conclusion

When converting decimals to fractions, and even to percent, it is good to know the math so that you can do it yourself if technology is not available. Keeping conversion charts handy can assist you in quickly finding data in the format you need for your work. Just take some time to compile the charts you need, bookmark them or print them. And work the math on a few to sharpen your skills. You will prove yourself more skilled at work if you can do math. It is not hard, you just need to try.