1Cademy - Procedure for Dividing Decimals

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Procedure for Dividing Decimals

To divide one decimal by another, convert the problem into an equivalent division with a whole-number divisor, then carry out long division. The Equivalent Fractions Property justifies shifting decimal points in both the dividend and divisor by the same number of places, because this amounts to multiplying the fraction $\frac{\text{dividend}}{\text{divisor}}$ by $\frac{10^n}{10^n} = 1$ . The five-step procedure is:

Determine the sign of the quotient: Apply the same rules as for integers — if the dividend and divisor share the same sign (both positive or both negative), the quotient is positive; if their signs differ, the quotient is negative.
Make the divisor a whole number: Move the decimal point in the divisor to the right until no decimal digits remain. Count the number of places moved.
Shift the dividend's decimal point the same number of places to the right: This keeps the quotient unchanged. Append placeholder zeros if the dividend does not have enough digits.
Divide and place the decimal point: Perform long division as though both numbers are whole numbers. Position the decimal point in the quotient directly above its new location in the dividend.
Write the quotient with the appropriate sign determined in Step 1.

This method reduces every decimal division problem to whole-number long division, with the decimal point's placement handled by a simple counting rule.

Updated 2026-05-02

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