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## Lesson 73:  Relationship Between Decimals and Fractions

In this lesson, we'll look at the relationship between decimals and fractions, and we'll see how they are really different ways of expressing the same thing.

First, review all of the previous lessons on fractions and decimals.  Make sure that you fully understand all of the material in those lessons.  Many students don't fully understand that decimals, fractions, and percents are all different ways of expressing the exact same thing.  We need all three ways, because sometimes one way just makes more sense than another.  You'll learn more about this later.

Remember that decimals are all based on tenths, hundredths, etc.  If you have a decimal, it's very easy to convert it to a fraction.  For example, what is 0.4 as a fraction?  It is 4/10 (four tenths).  That all we have do to.  If we'd like, we can reduce it to lowest terms like we've learned, and make it 2/5.  What is 0.07 as a fraction?  It is 7/100, and we're done.  What is 0.29 as a fraction?  That's two tenths and nine hundredths, but it's easier to look at it as twenty-nine hundredths, or 29/100.

Converting from a fraction to a decimal involves one extra step.  We need to convert the fraction so that it has a denominator of 10, or 100, or 1000, etc.  Then we can easily find its decimal equivalent.  For example, what is 2/5 as a decimal?  We'll multiply top and bottom by 2, giving us 4/10.  Now it is easy to write it as 0.4.  What is 13/25 as a decimal?  We'll multiply top and bottom by 4 to get 52/100, which is 0.52.  In later lessons, you'll learn what to do if you're given fractions to work with that aren't as simple as these, and you'll also learn how to convert those fractions to percents.

Remember that you can ask a math question if you have additional questions about a topic, or you can contact me if you have any comments or suggestions for this site.

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