Decimal to Fraction Converter
Converting decimals to fractions, or the reverse, is not always easy to do in your head or on paper. You will find help and save time with a decimal to fraction converter that simplifies the calculations for you.
What the Converter Widget Can Do
It may be easy to remember that 1/4 = 0.25 or that 1/2 = 0.5. However, there may be instances, such as reading an article, converting a recipe, or completing a do-it-yourself project, when you have unfamiliar or more complicated fractions and decimals and want to convert one to the other. The converter widget quickly changes decimals to fraction or vice versa.
Explaining Decimals and Fractions
A decimal number represents a part of 10, 100, 1000, and so on. A fraction, such as 8/3, is one number divided by (or over) another. The first, or top number, is the numerator, while the second, or bottom number, is the denominator, with the symbol "/" representing the division sign. The widget can quickly convert three types of fractions to decimals:
- Mixed fractions contain a whole number plus a fraction. For example, the mixed fraction 2 and 1/3 is written as 2 1/3 with a space between the whole number 2, and the fraction, 1/3.
- Proper fractions consist of just a numerator and denominator where the top number is smaller than the bottom number. For example, 1 over 4 is written as 1/4.
- Improper fractions are like proper fractions, except the numerator is larger than the denominator, resulting in a total value greater than 1. For example, 7 over 3 is written as 7/3. Such a fraction can be converted to a mixed fraction format as 2 1/3.
Using the Widget
The first part of the widget converts decimals to fractions:
- On the first line of the widget, enter your decimal number in the first box (e.g., 0.75).
- Click the "Calculate" button.
- The widget displays your result as a fraction (e.g., 3/4).
The second section converts fractions to decimals:
- If you have a mixed fraction (e.g., 2 1/3), enter the whole number (e.g., 2) in the first box. You skip this box if you have a proper or improper fraction without a whole number.
- In the next two boxes, enter your fraction like how you would write it on paper.
- In the top box, enter the numerator of your fraction.
- In the bottom box, enter the denominator of your fraction.
- Click "Calculate" to get your answer as a decimal.
Converting Decimals and Fractions
Fractions and decimals represent different ways to express parts of a whole number or thing. You can do a conversion of one to the other yourself using a few simple steps.
To Convert Decimal to Fraction
For example, to convert a decimal number, 0.6 to a fraction:
- To begin, think of 0.6 as a number over (divided by) the number 1.0. So, write 0.6 as the fraction 0.6/1.0.
- Next, change the numerator to a whole number by moving the decimals of both numerator and denominator the same number of places to the right. In this case, that's one space, equivalent to multiplying the top and bottom by 10.
- So, 0.6/1.0 is equivalent to 6/10
- In other examples of this math operation, you change decimal numbers that are in 1/100ths, 1/1000ths, and so on, to whole numbers by moving the decimals in the top and bottom by the same number of places to the right. For example: 0.06/1.0 = 6/100 (decimals moved two places to the right) and 0.006/1.0 = 6/1000 (decimals moved three places to the right).
- Finally, reduce the fraction to its lowest denominator by dividing it and numerator by their greatest common factor. This is the highest number they are both divisible by that will reduce both top and bottom to their lowest numbers:
- So, for 0.6 =6/10, the greatest common factor you can divide both 6 and 10 equally by is 2.
- Dividing both numbers by 2 reduces 6/10 to 3/5 (the two are equivalent fractions).
Thus, the decimal number 0.6 is re-written as 0.6/1.0. Moving the decimal place produces 6/10. Dividing the top and bottom by 2 results in the fraction 3/5.
To Convert Fraction to Decimal
You can convert a fraction to a decimal by using long division. Divide the numerator by the denominator with this simple approach:
- If the bottom of the fraction is bigger than the top, add a decimal place to the top and enough "0"s after it to make the numerator bigger than the denominator (ignoring the decimal place for the moment). Then, proceed with your division.
- For example, starting with the fraction 9/15:
- Add a decimal and "0" to the 9, so 9/15 = 9.0/15.
- Next, since you can't divide 9.0 by 15, instead divide 90 by 15. The answer is 6.
- Because the actual number is 9.0 and not 90, add a decimal before the 6 to get the answer 0.6.
In summary, the fraction 9/15 is equal to 9.0/15, which calculates to 0.6, its decimal equivalent.
A Convenient and Accurate Tool
Free online tools save you money, effort and time. Our widgets, such as this decimal to fraction converter, are accessible and easy to use on any device. Rely on them to give you accurate results every time.