Subjects arithmetic

Decimal Division

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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.