How to Convert Decimals to Fractions
Whether it’s homework for a grade school student or a business problem, math is an essential skill in life. One of the most common math problems is converting decimals to fractions. You don’t need to buy an expensive calculator or to manipulate a sophisticated computer program to convert decimals to fractions. All you need is mathematical know-how, a pen and paper, and a mathematical problem.
What are Decimals?
calculatorThe decimal system is the most commonly used numeral system in the world. Decimals have the number 10 as their base, and it is widely accepted that the 10 numbers of the decimal system correspond to each digit in the hand. A decimal value is denoted by a dot that separates a whole value from a fractional value. The fractional value is a portion of the whole unit that can be expressed in a fraction form.
Decimal values are divided into different positions, each corresponding to a value in base 10. To the left of the decimal point are the places for ones, tens, hundreds, thousands, and so on. To the right of the decimal point are the places for tenths, hundredths, thousandths, and so on.
A decimal value like 34.875 means:
Three tens
Four units
Eight tenths
Seven hundredths
Five thousandths
What are Fractions?
A fraction is the relationship between the whole quantity and the portion derived from it. A fraction has two parts:
The numerator is the quantity derived from the whole.
The denominator is the quantity of the whole.
The value of the fraction is obtained when the value of the numerator is divided by the value of the denominator. A fraction is a lot like a division problem, where the value of fractions are portions of a divided whole number or quantity. Fractions are written as division problems, with the quotient expressed as a decimal value.
For a fraction like 5/8:
Five is the dividend
Eight is the divisor
When the dividend is divided by the divisor, the result is 0.625
Converting Decimals to Fractions
Converting decimals to fractions is easy. You do not need a really powerful computer or an expensive scientific calculator to complete a decimal-to-fraction conversion problem. You only need to follow three steps:
Write the decimal as a fraction divided by 1.
Multiply the numerator and denominator by 10 for every decimal place after the decimal point.
If necessary, reduce the resulting fraction to its simplest form.
If you want to convert 0.25 into a fraction, for example:
Express the decimal in fraction form: 0.25/1.
Multiply both the numerator and the denominator by 100, because 0.25 has two decimal places: (0.25 x 100) / (1 x 100). The end result should be 25/100.
The greatest common factor (GCF) of 25 and 100 is 25, because it is the biggest number that divides exactly between the two values. To simplify the fraction, you simply divide 25 over 25 and 100 over 25.
The decimal value 0.25 is then expressed in the fraction 1/4.
The method for converting fractions to decimals is the same for just about any number, except for repeating or recurring decimal expressions (like 0.33333 and 0.4545454545). With these simple hints and tricks, you don’t have to worry about having to grapple with complicated conversion problems anymore.