Decimal Division
1. Problem statement: Compute $7.2 / 0.8$.
2. Strategy and formula: To divide decimals, multiply both numbers by the same power of 10 to make the divisor an integer.
Use the identity $a / b = (a \times 10^n) / (b \times 10^n)$ where $n$ makes $b \times 10^n$ an integer.
3. Remove the decimals by multiplying numerator and denominator by 10: $7.2 \times 10 = 72$ and $0.8 \times 10 = 8$.
So the problem becomes $72 / 8$.
4. Long division of $72$ by $8$.
Consider the first digit $7$; since $7 < 8$ we take the first two digits $72$.
Determine how many times $8$ fits into $72$: $9$ times because $9 \times 8 = 72$.
Write $9$ as the quotient digit.
Multiply and subtract: $72 - 72 = 0$ remainder.
Since there are no more digits to bring down and the remainder is $0$, the division ends.
5. Final answer: $7.2 / 0.8 = 9$.
Explanation: Converting to whole numbers made the long division straightforward and showed the quotient exactly.