Chapter 9
MULTIPLYING DECIMALS
What are decimals?
All numbers are made up of digits: 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. Digits are like letters in a word. A
word is made up of letters. Numbers are made up of digits: 23 is a two-digit number, made from the
digits 2 and 3; 627 is a three-digit number made from the digits 6, 2 and 7. The position of the digit in
the number tells us its value. For instance, the 2 in the number 23 has a value of 2 tens, and the 3 has a
value of 3 ones. Numbers in the hundreds are three-digit numbers: 435, for example. The 4 is the
hundreds digit and tells us there are 4 hundreds (400). The tens digit is 3 and signifies 3 tens (30). The
units digit is 5 and signifies 5 ones, or simply 5.
When we write a number, the position of each digit is important. The position of a digit gives that
digit its place value.
When we write prices, or numbers representing money, we use a decimal point to separate the dollars
from the cents. For example, $2.50 represents 2 dollars and 50 hundredths of a dollar. The first digit
after the decimal represents tenths of a dollar. (Ten 10¢ coins make a dollar.) The second digit after the
decimal represents hundredths of a dollar. (One hundred cents make a dollar.) So $2.50, or two and a
half dollars, is the same as 250¢. If we wanted to multiply $2.50 by 4 we could simply multiply the
250¢ by 4 to get 1,000¢. One thousand cents is the same as $10.00.
Digits after a decimal point have place values as well. The number 3.14567 signifies three ones, then
after the decimal point we have one tenth, four hundredths, five thousandths, six ten-thousandths, and so
on. So $2.75 equals two dollars, seven tenths of a dollar and five hundredths of a dollar.
To multiply a decimal number by 10 we simply move the decimal point one place to the right. To
multiply 1.2 by 10 we move the decimal one place to the right, giving an answer of 12. To multiply by
100, we move the decimal two places to the right. If there aren’t two digits, we supply them as needed
by adding zeros. So, to multiply 1.2 by 100, we move the decimal two places, giving an answer of 120.
To divide by 10, we move the decimal one place to the left. To divide by 100, we move the decimal
two places to the left. To divide 14 by 100 we place the decimal after the 14 and move it two places to
the left. The answer is 0.14. (We normally write a 0 before the decimal if there are no other digits.)
Now, let’s look at general multiplication of decimals.
Multiplication of decimals
Multiplying decimal numbers is no more complicated than multiplying any other numbers. Let us take
an example of 1.2 × 1.4.
We write down the problem as it is, but when we are working it out we ignore the decimal points.
Although we write 1.2 × 1.4, we treat the problem as:
12 × 14 =
We ignore the decimal point in the calculation; we calculate 12 plus 4 is 16, times 10 is 160. Four
times 2 is 8, plus 160 is 168.
The problem will look like this: