The Decimal System
The system of numbers that you use is called the decimal system and is based on
powers of ten ( base ten system). Each place in the place value grid is ten times
the value of the place to the right of it. Every number to the right of the decimal
point is a decimal fraction (a fraction with a denominator of 10, 100, 1,000, and so
on). Notice that there is no “oneth” place value.
Example 1:
Writing decimals
To read a decimal or write a decimal in words, you start at the left and end with
the place value of the last number on the right. Where a whole number is included,
use the word “and” to show the position of the decimal point.
Example 3: Read the number
.75
Example 4: Read the number
45.321
Example 5: Write two hundred and three tenths.
Comparing decimals
If you want to compare decimals, that is, find out if one decimal is greater than
another, simply make sure that each decimal goes out to the same number of places
to the right.
Example 6: Which is greater, .37 or .365?
Remember, this is the same as comparing 37/100 and 365/1000 you can’t really
compare them unless you have the same denominator.
It is easy to see that .37 is greater. You are really comparing three hundred
seventy thousandths to three hundred sixty-five thousandths.
Example 7: Put the decimals .66, .6587, and .661 in order from largest to smallest.
First, change each number to ten-thousandths by adding zeros where appropriate.
Then align the decimal points to make the comparison.
The order should be .661, .66, and .6587.
You can also align the decimals first and then add the zeros as follows.
Remember: The number of digits to the right of the decimal point does not
determine the size of the number (.5 is greater than .33).
Rounding decimals
The method for rounding decimals is almost identical to the method used for
rounding whole numbers. Follow these steps to round off a decimal:
1. Underline the place value to which you're rounding.
2. Look to the immediate right (one place) of your underlined place value.
3. Identify the number (the one to the right). If it is 5 or higher, round
your underlined place value up 1 and drop all the numbers to the right of
your underlined number. If the number (the one to the right) is 4 or
less, leave your underlined place value as it is and drop all the numbers
to the right of your underlined number.
Example 8: Round off
.478 to the nearest hundredth.
Example 9: Round off 5.3743 to the nearest thousandth.
Adding and subtracting decimals
To add or subtract decimals, just line up the decimal points and then add or
subtract in the same manner you would add or subtract whole numbers.
Example 1: Add 23.6 + 1.75 + 300.002.
Adding in zeros can make the problem easier to work.
Example 2: Subtract 54.26 − 1.1.
Example 3: Subtract 78.9 − 37.43.
A whole number has an understood decimal point to its right.
Example 4: Subtract 17 −8.43.
Multiplying decimals
To multiply decimals, just multiply as usual. Then count the total number of digits
above the line which are to the right of all decimal points. Place your decimal point
in your answer so there is the same number of digits to the right of it as there was
above the line.
Example 5: Multiply 40.012 × 3.1.
Dividing decimals
Dividing decimals is the same as dividing other numbers, except that if the divisor
(the number you're dividing by) has a decimal, move it to the right as many places
as necessary until it is a whole number. Then move the decimal point in the dividend
(the number being divided into) the same number of places. Sometimes, you may
have to add zeros to the dividend (the number inside the division sign).
Example 6: Divide
Example 7: Divide
Example 8: Divide