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 .
