How to Change a Mixed Number into a Decimal

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Fractions and decimal numbers are both extremely common ways of presenting numerical information. Each is commonly used in writing quantities that are not whole numbers, such as those that are not in the set {... , −3, −2, −1, 0, 1, 2, 3, ...}. Both are useful for expressing numbers that are not "round" or "neat."

At times, you may need to convert between fractions and decimal numbers. This process can become a little more complicated when the fraction you start with is a special kind of fraction called a mixed number. By converting mixed fractions to other kinds of fractions, you set yourself up to convert it to a decimal number in a single easy step.

What Are Fractions?

A fraction is written a/b where a and b are integer numbers. a is called the numerator and b the denominator. When a < b, the fraction is a proper fraction; when a ≥ b (that is, when a is greater than or equal to b), the fraction is an improper fraction and can be modified into a mixed number, as you'll see.

Fractions are used to convey the concept of "share" or ratio. For example, if you have a box of 12 donuts, and give 6 to your friends and 2 to your parents while keeping 4 for yourself, the fraction of donuts you gave to your friends is 6/12, the fraction you gave to your folks is 2/12, and the fraction you saved for your own snacking is 4/12.

What Is a Mixed Number?

Also called a mixed fraction, a mixed number consists of an integer part and a fractional part.

How to Convert a Mixed Number to an Improper Fraction

Say you are given the mixed fraction 17 2/3 and asked to convert it to an improper fraction. How would you go about doing this?

The first step is to multiply the number in the denominator of the fraction by the integer number. This step gives (3)(17) = 51.

Next, add the numerator to this total, giving the numerator for the improper fraction you are creating. This step gives 51 + 2 = 53.

Finally, use the same denominator as in the mixed number to write the improper fraction, in this case 53/3.

What Is a Decimal Number?

Any handling of U.S. currency you have done has familiarized you with the basic concept of decimal numbers. For example, $2.18 is "two point one eight dollars," though you probably said something different to convey this information.

A decimal is the name for a period between the end of a whole number and any remainder the number has. For example, 34.17 is 34 plus 17 units out of 100 for the remainder.

In a decimal number, the first place to the right of the decimal is for tenths (1/10), the second place for hundredths (1/100) and so on, making for a convenient system given that there are ten digits in use (0 through 9).

How to Convert an Improper Fraction to a Decimal

Now that you have your original mixed number in the form of an improper fraction, you are ready to solve the problem. All you need to do is divide, and a standard calculator will return an answer in decimal-number form.

In the case of 53/3, the answer is 17.6666... The trailing periods indicate that the 6 is an endlessly repeating digit in the case of this decimal number. This can be written by placing a bar over the repeating digit. In some cases, a group of digits may repeat, as in the case of 9/7, which has the solution 1.285714285714...

Convert a Mixed Fraction to a Decimal Online

See the Resources for a page that allows you to convert a mixed number into a fraction automatically into a single step.

References

Resources

About the Author

Kevin Beck holds a bachelor's degree in physics with minors in math and chemistry from the University of Vermont. Formerly with ScienceBlogs.com and the editor of "Run Strong," he has written for Runner's World, Men's Fitness, Competitor, and a variety of other publications. More about Kevin and links to his professional work can be found at www.kemibe.com.

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