Understanding decimals

Understanding decimals starts with a good understanding of decimal place value. Therefore, I recommend that you start by carefully studying decimals place value before studying the other lessons on this page. 


Once you are done reading this introduction about decimals, you can start studying the other lessons in the order given.

What is a decimal? When examining the word decimal, you can recognize the prefix deci. And deci is equal to 1/10 or 0.1

Generally speaking though, a decimal is referring to any proper or improper fraction whose denominator is 10, 100, 1000, and so forth...

For example, the following are all examples of decimals.

5/10  = 0.5

2/100 = 0.02

16/1000 = 0.016

1/100  = 0.01

195/10000  = 0.0195

45/10 = 4.5

234/100  = 2.34

Notice that the first 5 are proper fractions and the last two are improper fractions.

A few important terminology to keep in mind about the decimals.

  • A proper fraction whose denominator can be written as a power of 10 is called a decimal fraction. 5/10 = 0.5 and 16/1000 = 0.016 are examples of decimal fractions.
  • An improper fraction whose denominator can be written as a power of 10 is called a mixed decimal. 45/10 = 4.5 and 234/100 = 2.34 are examples of mixed decimals.
  • We can say that a decimal is a combination of a whole number and a fraction of a whole number.
  • Notice also that a whole number is also a decimal. For example, 69 can also be written as 69.0 since 69 = 69.0.

More lessons about understanding decimals  

Decimals place value
Learn how to name the place value of a decimal number.

Writing decimals in words
Learn how to read and write decimals.

Comparing decimals
Learn how determine if a decimals is bigger or smaller than another decimal.

Rounding decimals
Learn how to simplify a decimal number by rounding.

Adding decimals
This lesson will attempt to give you a deep understanding of adding decimals.

Subtracting decimals
A deep understanding of subtraction with decimals.

Decimals to fractions
Learn how to convert a decimal number to a fraction.

Fractions to decimals
Learn how to convert a fraction to a decimal.

Converting repeating decimals to fractions
Learn how to convert repeating decimals to fractions.

Ways of writing decimals
Learn about the six different ways of writing decimals.

Writing decimals in words
Learn how to write a decimal in word form.

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