Dividing by a Decimal

Dividing by a decimal is awkward, but dividing by a whole number is not. So turn the divisor into a whole number first. In $\frac{6.3}{0.9}$, move the point one place right in both numbers, which multiplies both by 10. That gives $\frac{63}{9}$, which is 7.

Why is that allowed? Multiplying the top and the bottom of a fraction by the same number gives an equal fraction, as you saw in Factors and Fractions. A division is a fraction, so $\frac{6.3}{0.9}$ and $\frac{63}{9}$ have the same value. Moving only one of the points would change the value tenfold.

Move the points as many places as the divisor needs to become whole, and move the top number the same distance. For a divisor with two places, both points move two places: $\frac{0.5}{0.25}$ becomes $\frac{50}{25}$, which is 2.