Dividing Decimals Formula
Dividing decimals are dividing numbers that contain decimal points, typically by converting the divisor to a whole number (multiplying both divisor and.
The Formula
When to use: If you want to split $7.20 equally among 3 people, you're dividing a decimal. The trick for harder problems is: if the divisor is , multiply both numbers by 10 to get . You haven't changed the answer—just made it easier to compute.
Quick Example
Notation
What This Formula Means
Dividing numbers that contain decimal points, typically by converting the divisor to a whole number (multiplying both divisor and dividend by a power of 10) and then performing long division.
If you want to split $7.20 equally among 3 people, you're dividing a decimal. The trick for harder problems is: if the divisor is , multiply both numbers by 10 to get . You haven't changed the answer—just made it easier to compute.
Formal View
Worked Examples
Example 1
easyAnswer
First step
Full solution
- 2 Since , we get .
- 3 Or: ✓.
Example 2
mediumExample 3
mediumCommon Mistakes
- Shifting only one number's point - move both decimal points the same number of places.
- Shifting unequal numbers of places - shift exactly enough to make the divisor whole, same shift on both.
- Misplacing the decimal in the quotient - line the answer's point up above the dividend's shifted point.
Why This Formula Matters
It rests on a fairness idea: multiplying top and bottom by the same power of 10 doesn't change the quotient, just like equivalent fractions. Students who shift only one number, or shift unequal amounts, silently change the answer. Recognizing it by "Is the divisor a decimal I should make whole by shifting both points equally?" — rather than by familiar numbers — is what lets a student tell it apart from multiplying decimals and adding/subtracting decimals and whole-number long division in a mixed problem set.
Frequently Asked Questions
What is the Dividing Decimals formula?
Dividing numbers that contain decimal points, typically by converting the divisor to a whole number (multiplying both divisor and dividend by a power of 10) and then performing long division.
How do you use the Dividing Decimals formula?
If you want to split $7.20 equally among 3 people, you're dividing a decimal. The trick for harder problems is: if the divisor is , multiply both numbers by 10 to get . You haven't changed the answer—just made it easier to compute.
What do the symbols mean in the Dividing Decimals formula?
Move the decimal point in both divisor and dividend the same number of places to the right until the divisor is a whole number
Why is the Dividing Decimals formula important in Math?
It rests on a fairness idea: multiplying top and bottom by the same power of 10 doesn't change the quotient, just like equivalent fractions. Students who shift only one number, or shift unequal amounts, silently change the answer. Recognizing it by "Is the divisor a decimal I should make whole by shifting both points equally?" — rather than by familiar numbers — is what lets a student tell it apart from multiplying decimals and adding/subtracting decimals and whole-number long division in a mixed problem set.
What do students get wrong about Dividing Decimals?
The procedure for dividing decimals is the easy part; the trap is shifting only one number's point. Asking "Is the divisor a decimal I should make whole by shifting both points equally?" first is what keeps a correct-looking calculation from being attached to the wrong concept.
What should I learn before the Dividing Decimals formula?
Before studying the Dividing Decimals formula, you should understand: division, long division, place value.