Dividing a whole number by a decimal is understood as finding how many groups of the decimal-sized quantity are contained in the whole number, including quotients greater than the dividend when the divisor is less than one. Learners use place-value reasoning to multiply both dividend and divisor by the same power of ten, convert the divisor to a whole number, and verify the result through estimation and multiplication; the focus is on finite decimal divisors and quotients, not repeating-decimal or fully generalized rational division.
To divide a whole number by a decimal, find how many groups of the decimal amount fit into the whole number.
Example: Find .
Estimate. Since is less than , the answer should be greater than . In fact, about ten groups of make , so the answer will be around .
Make the divisor a whole number. Move the decimal point in one place to the right to get . Because you moved the divisor one place, also multiply the dividend by :
So,
The answer is correct because groups of equal . When the divisor is less than , the quotient can be greater than the whole-number dividend.
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