The Basics of Decimals Study Guide

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Updated on Oct 3, 2011

Introduction to The Basics of Decimals

Decimals have a point.

—Author Unknown

In this article, you'll learn about the wonders of a simple decimal point, how to perform operations on decimals, and how to convert between decimals and fractions.

The Decimal System is a way to name numbers based on the powers of 10. The numbers to the right of the decimal point are fractional equivalents with denominators that are powers of ten. For example,

Decimals are based on the place value of our number system where position from the decimal point has meaning:


Note the pattern of how the names of the decimal places to the right of the decimal are similar to the names of the place values to the left of the decimal point. Keep the mental image of the decimal point pairing up with the "ones" place in order to easily remember the place value names.

The decimal number 1.52 is read as "one and fifty-two hundredths," or . The number 0.05 is read as "five hundredths," or .

Decimal numbers are easy to compare and order, when you remember that the place value has meaning. In mathematics, 2.4 is the same number as 2.400 because both numbers represent "two and four tenths." A whole number is understood to have a decimal point to the right of the number. For example, 12 = 12. = 12.0 = 12.000. Each expression represents twelve with no remainder. To compare decimals, it is best to change each decimal into an equivalent decimal with the same number of decimal places.

Try ordering the numbers from least to greatest: .016, 0.7, .203, .75 Because some of the numbers have three places to the right of the decimal point, change each decimal to an equivalent decimal with three decimal places to the right of the decimal point. One of the numbers shows a leading zero; also include this leading zero in all of the numbers:

0.016, 0.700, 0.203, 0.750

Now the decimals can be compared in the same manner as whole numbers, and 16 < 203 < 700 < 750, so the answer is .016, .203, 0.7, .75.

Operations and Decimals

To add or subtract decimal values, line up the decimal points and add or subtract.


When you are multiplying decimals, first you multiply in the usual fashion, and then count over the proper number of places. This is done by counting how many places are to the right of the decimal points in each number you are multiplying.


When you are dividing decimals, you move the decimal point of the dividend and divisor the same number of places.


Decimals and Fractions

Decimals and fractions are two different ways to represent the same values. In other words, you can equate fractions and decimals. Let's look at the relationship between the fraction and the decimal 0.1. The following figure represents both values.


To convert a fraction to a decimal, just divide the top by the bottom. Look at the fraction ; 1 ÷ 2 = 0.5, so is equal to 0.5.


In case you are asked to convert a fraction to a decimal, you should have some common conversions memorized.

Fraction Decimal

Find practice problems and solutions for these concepts at The Basics of Decimals Practice Questions.

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