Understanding Decimals – fractioncalculation.com

In order to better understand decimals, you need to know what decimals are in the first place.

Simply put, a decimal is just a number that is expressed in the scale of tens. If you are looking for a more familiar language, then you can say that decimal numbers include a decimal point to represent a whole number and a fraction of a whole number (tenths, hundredths, etc.

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The decimal point is just the dot or point that is used to separate the whole part of a number from its fractional part.

If you take a closer look at the decimal word, you can easily recognize the prefix deci that means equal to 1/10 or 0.1.

However, generally speaking, a decimal refers to any fraction (either proper or improper) that comes with a denominator that is 10, 100, 1000, and so forth.

Here are some 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

If you look closely, you can see that while the first 5 are proper fractions, the last 2 are improper fractions.

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Decimals Terminology

There are some things that you need to keep in mind about decimals terminology:

A proper fraction whose denominator can be written as a power of 10 is called a decimal fraction. Some examples include 5/10 = 0.5 and 16/1000 = 0.016.
An improper fraction whose denominator can be written as a power of 10 is called a mixed decimal. Some examples include 45/10 = 4.5 and 234/100 = 2.34.
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.

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The Decimal Place Value

When talking about decimals, you need to know what the decimal place value is.

In the number 15.43258, the place value for 4 is the tenths.

Note that 1 tenth = 0.1 or 1/10, so 4 tenths means 4 × 0.1 or 0.4.

Besides, in the number 15.43258, the place value for 2 is the thousandths.

1 thousandth = 0.001 or 1/1000, so 2 thousandths means 2 × 0.001 or 0.002.

There is another way to look at it and extract 0.002 from 15.43258.

All you need to do is to write down the 2 and then replace all the other numbers to the left of 2 with 0. You get 00.002 and looking at 00.002, you can get rid of the extra zero on the left. Notice that the last number that will be replaced with a zero is the one right before the number 2. Finally, as you can see, you still get the same answer of 0.002.

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