Step 1: Estimate the answer by rounding . You'll use this estimate to check your answer later.
Step 2: If the divisor is not a whole number, then move the decimal place n
n
places to the right to make it a whole number. Then move the decimal place in the dividend the same number of places to the right (adding some extra zeros if necessary.)
Step 3: Divide as usual. If the divisor doesn't go in evenly, add zeros to the right of the dividend and keep dividing until you get a 0
0
remainder, or until a repeating pattern shows up.
Step 4: Put the decimal point in the quotient directly above where the decimal point now is in the dividend.
Step 5: Check your answer against your estimate to see if it's reasonable.
Example:
Divide.
0.45÷3.6
0.45
÷
3.6
Step 1: Since the divisor is greater than the dividend, we will get an answer less than 1
1
. Since 0.45
0.45
is about one tenth as big as 3.6
3.6
, we expect an answer close to 0.1
0.1
.
Step 2: The divisor is not a whole number, so move the decimal point one place to the right to make it a whole number. Move the decimal point in the dividend one place to the right also.
364.5
36
4.5
Step 3: Divide normally, adding extra zeros to the right of 4.5
4.5
when you run out.
361254.50036⎯⎯⎯⎯⎯9072⎯⎯⎯⎯180180⎯⎯⎯⎯⎯⎯0
36
125
4.500
3
6
_
90
72
_
180
180
_
0
Step 4: Put the decimal point in the quotient directly above the decimal point in the dividend.
360.1254.50036⎯⎯⎯⎯⎯9072⎯⎯⎯⎯180180⎯⎯⎯⎯⎯⎯0
36
0.125
4.500
36_90 72_180 180_0
We get 0.125
0.125
.
Step 5: Compare with your initial estimate. 0.125
0.125
is close to 0.1
0.1
, so we're good!
Sometimes, it's easier to use mental math to solve a decimal division problem. This is a good strategy when you can see that if you move the decimal points around, you can change the problem into one you've memorized the answer to.
Example:
Divide.
0.42÷700.42÷70
We know that 42÷7=6
42÷7=6.
If the dividend is decreased by a factor of 10
10
, then the quotient will also decrease by a factor of 10
10
.
42÷7=64.2÷7=0.60.42÷7=0.06 42÷7=6 4.2÷7=0.6 0.42÷7=0.06
And if the divisor is increased by a factor of 10
10
, then the quotient will decrease by a factor of 10
0.42÷70=0.006
0.42÷70=0.006
So, the answer is 0.006