Division of positive decimals is understood as determining how many groups of a decimal size are contained in another quantity, or finding an unknown factor in a multiplication relationship. The quotient remains unchanged when both dividend and nonzero divisor are multiplied by the same power of ten, allowing place-value reasoning and the standard algorithm; estimates help detect misplaced decimal points. The scope includes finite decimals and reasonable approximations to hundredths, not more advanced algebraic or infinite-decimal treatments.
To divide by a decimal, make the divisor a whole number. Multiply both the dividend and divisor by the same power of . This keeps the quotient unchanged.
Example: Find .
Estimate first.
Since and , the answer should be around .
Make the divisor a whole number.
The divisor, , has two digits after the decimal point, so multiply both numbers by :
Divide.
Therefore,
So,
The answer makes sense because is reasonably close to the estimate of .
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