Call Now: (800) 537-1660

May 25th

May 25th

# Decimals and their Equivalent Fractions

Question: What is the equivalent fraction for the decimal 4.422?

 Misconception The common misconception here is that decimals and fractions are different typesof numbers. Hence there is no equivalent fraction for this or any other decimal. Correct You can express the decimal as 4 and (the fraction) . These are fraction equivalents. These can be simplified by dividing both numerator and denominator by 2 to give

Further Explanation

The method above shows how to obtain an equivalent fraction from a decimal. It is even easier to find the decimal equivalent of a fraction. All you have to do is to use division.

So, for example, the decimal equivalent of the fraction is 0.25 as 1.00 divided by 4 will give this result. Similarly the fraction can be expressed as a decimal by dividing 3 by 5 to obtain 0.6

A similar way of achieving this is to find an equivalent fraction that has either 10 or 100 or 1000 etc. as the denominator. In this way we can determine the fraction equivalent from the resulting numerator. For example,

and so the decimal equivalent is 0.6.

Similarly for more complicated fractions such as . We can find its decimal equivalent by multiplying both numerator and denominator by 25. This gives

and so the decimal equivalent is 0.075

If you are still feeling confused about equivalent decimals and fractions, then think of a number line in which all numbers are represented. A small part of such a number line is shown below with numbers shown as decimals above the line and fractions below the line

You can readily see, for example, that

Note: What happens when the fraction cannot be expressed as an equivalent fraction with a numerator of 10 or 100 or 1000 etc.?

An example of this is the fraction . You can though divide 1.0000000......... by 3 to give 0.33333.......... This is called a recurring decimal, and is often denoted by putting a dot on top of the number (or numbers) that repeat. So we can write

There are many other fractions that give rise to recurring decimals, often with a group of digits that repeat. For example

Free Tutoring
• Get 30 Minutes of FREE Live Tutoring from Tutor.com if you

Testimonials
"I ordered the Algebra Buster late one night when my daughter was having problems in her honors algebra class. After we ordered your software she was able to see step by step how to solve the problems. Algebra Buster definitely saved the day."
Tami Garleff

Home    Why Algebra Buster?    Guarantee    Testimonials    Ordering    FAQ    About Us
What's new?    Resources    Animated demo    Algebra lessons    Bibliography of     textbooks