Standard Algorithm with Decimal Divisors

Property To divide by a decimal, first convert the divisor into a whole number by multiplying both the divisor and the dividend by the same power of 10. This is equivalent to moving the decimal point in both numbers the same number of places to the right. Then, perform division as usual. $a \div b = (a \times 10^n) \div (b \times 10^n)$.

Examples To solve $9.6 \div 0.8$, we can rewrite it as $96 \div 8$. The quotient is $12$. To solve $15.75 \div 0.25$, we multiply both numbers by $100$ to get $1575 \div 25$. The quotient is $63$. To solve $4.83 \div 0.7$, we multiply both numbers by $10$ to get $48.3 \div 7$. The quotient is $6.9$.

Explanation This skill applies the standard division algorithm directly to problems with decimal divisors. The first step is to make the divisor a whole number by moving its decimal point to the right. You must then move the decimal point in the dividend the same number of places to the right to keep the problem equivalent. After adjusting the decimal points, place the decimal for the quotient directly above its new position in the dividend and divide as you would with whole numbers.