Chapter 4 Notes
Multiplying Decimals
How to multiply decimals by 10,100, and 1000



Count the number of zeros in the multiplier
Move the decimal point in the number you are multiplying to the right one place for each zero
Write as many zeros in the product as needed
Examples
10 x 0.56 = 5.6 (10 has one zero so move the decimal point 1 place to the right)
100 x 0.56 = 56 (100 has two zeros so move the decimal point 2 places to the right)
1000 x 0.56 = 560 (1000 has three zeros so move the decimal point 3 places to the right and you
need one zero as a placeholder)
How to multiply decimals by whole numbers



Multiply as you would with a whole number
Count the number of digits to the right of the decimal point
Place the decimal point that many places in from the right in your answer
Example
0.68
X 48
544
2720
32.64
When you multiply as if they are whole
numbers, you get 3264. Since 0.68 has two
decimal places, you place the decimal point
two places in from the right on the answer.
How to multiply a decimal by a decimal



Multiply as you would with whole numbers
Count the number of decimal places in both factors
Place the decimal point that many places in from the right in your answer
Examples
14.3
X 0.75
715
10010
10.725
When you multiply as if they are whole
numbers, you get 10725. Since 14.3 has
one decimal place and 0.75 has two, you
move the decimal point in your answer over
3 places from the right.
0.38
X 0.02
0.0076
$72.25
X 0.75
36125
505750
$54.1875
When you multiply as if it is a whole number, you get 76. Since 0.38 and 0.02 each of
two decimal places, you need to move the decimal point in 4 places to the right. Since
there are only 2 place values in the answer, you need to add 2 zeros.
Since this is money, you need to round to the hundredths place. Since 7 is greater than
5, the 8 in the hundredths place rounds up to a 9.
Dividing Decimals
How to divide a decimal by 10, 100, or 1000



Count the numbers of zeros in the divisor
Move the decimal point to the left in the number you are dividing one place for every zero in the
divisor
Write zeros in the quotient (answer)as needed
Examples
68.4 ÷ 10= 6.84 (10 has one zero so move the decimal point 1 place to the left)
68.4 ÷ 100= 0.684 (100 has two zeros so move the decimal point 2 places to the left)
68.4 ÷ 1000= 0.064 (1000 has three zeros so move the decimal point 3 places to the left and a 1
zero as a placeholder)
How to divide a decimal by a whole number


Write the decimal point in the quotient directly above the decimal point in the dividend
(number being divided)
Divide as you would with whole numbers
Examples
$3.11
6 $18.66
-18
06
-6
06
-6
0
0.48
3 1.44
-12
24
- 24
0
2.19
4 8.76
-8
07
-4
36
-36
0
How to divide a decimal by a decimal




Move the decimal point in the divisor (number outside division square) to form a whole number
divisor
Move the decimal point in the dividend (number inside the division square) to the right the
same number of places
Place the decimal point in the quotient (answer)
Divide. Add zeros to the quotient and dividend as needed.
Examples
6.2
0.4 2.48
-24
08
- 8
0
0.53
2.4 1.272
- 120
72
- 72
0
0.048
0.5 0.0240
- 20
40
- 40
0