Decimal Division Practice

First identify the dividend and divisor. In 8.4 ÷ 4, the dividend is 8.4 and the divisor is 4. Because the divisor is a whole number, ordinary division works directly. Eight units shared into four groups gives two units in each group. Four tenths shared into four groups gives one tenth in each. Together each group contains 2.1.

A decimal divisor is often easier to handle after writing an equivalent calculation. Multiply the divisor by a power of ten that makes it whole. Multiply the dividend by exactly the same amount. For 6.72 ÷ 0.8, multiplying both numbers by ten gives 67.2 ÷ 8. The quotient stays unchanged because the two quantities have been scaled equally.

Why does equal scaling work? A division can be written as a fraction, with the dividend above the divisor. Multiplying its numerator and denominator by the same nonzero number produces an equivalent fraction. Changing only the divisor would produce a different fraction and therefore a different answer. Write both transformed numbers before starting the long division.

If you need more digits while dividing, add zeros to the end of the dividend after its decimal point. They provide further places to divide without altering its value. Continue until the remainder is zero for a terminating answer. Some divisions repeat forever, but the questions in this tool are chosen to terminate, so no unstated approximation is required.

Use the size of the divisor to judge your result. Dividing a positive number by 0.5 asks how many halves fit into it, so the quotient is twice the dividend. Dividing by 10, 100, or 1000 instead reduces each digit’s place value by one, two, or three places. Finish by multiplying the quotient by the divisor. Their product should equal the original dividend exactly.