- Simplify the division: Multiply both numbers by 10 to get \(753.3 \div 93\).
- Calculate the quotient: Performing the division \(753.3 \div 93\) yields \(8.1\).
- Estimate for accuracy: Round \(9.3\) to \(9\) and \(75.33\) to \(72\); calculating \(72 \div 9 = 8\) confirms the result is reasonable.
- Final answer: The calculated quotient is \(\boxed{8.1}\).
Explanation
- Performing the Division
To divide \(75.33\) by \(9.3\), we first simplify the expression to make the division easier. The dividend is \(75.33\) and the divisor is \(9.3\). We can multiply both numbers by \(10\) to eliminate the decimal in the divisor, which changes the problem to calculating \(753.3 \div 93\).
To perform the long division:
- Divide \(753\) by \(93\): \(93 \times 8 = 744\).
- Subtract \(744\) from \(753\), which leaves \(9\).
- Bring down the next digit, \(3\), to make it \(93\).
- Divide \(93\) by \(93\): \(93 \times 1 = 93\).
- The decimal point is placed correctly, resulting in \(8.1\).
Thus, the result of the division \(75.33 \div 9.3\) is \(8.1\).
- Estimating for Reasonableness
To ensure the result is reasonable, we perform an estimation. We can round the divisor \(9.3\) to the nearest whole number, which is \(9\). For the dividend \(75.33\), we can round it to a multiple of \(9\) that is nearby, such as \(72\).
Performing the division with the estimated numbers:
\[72 \div 9 = 8\]
Since \(8.1\) is very close to our estimate of \(8\), the calculation is reasonable and likely correct.
- Conclusion
By performing both the precise division and the estimation check, we have determined the quotient. The division of \(75.33\) by \(9.3\) is \(8.1\), which aligns well with our estimate. Therefore, the final result is \(\boxed{8.1}\).
Examples
Imagine you are buying bulk items, such as packets of seeds for a garden. If the total cost for \(9.3\) kilograms of seeds is \(\$75.33\), you can use this division to find the price per kilogram. By calculating \(\$75.33 \div 9.3 \text{ kg}\), you determine that the seeds cost \(\$8.10\) per kilogram. This helps in budgeting and comparing prices between different bulk options to ensure you get the best deal for your gardening project.