Verified Answer :

  • Represent the division as a fraction: \(\frac{9.36}{0.4}\).
  • Multiply both numerator and denominator by 10 to make the divisor an integer: \(\frac{93.6}{4}\).
  • Perform the division of 93.6 by 4.
  • The result of the division is \(\boxed{23.4}\).

Explanation

  1. Problem Analysis

The objective is to compute the division of two decimal numbers, \(9.36\) and \(0.4\). We are asked to evaluate the quotient \(9.36 \div 0.4\). Decimal division can be approached by converting the divisor into an integer, which simplifies the division process.

  1. Adjusting the Expression

To eliminate the decimal point in the divisor, we can multiply both the dividend and the divisor by a power of ten. Since the divisor \(0.4\) has one decimal place, multiplying both numbers by \(10\) will shift the decimal point one position to the right, maintaining the same ratio:
\[\frac{9.36}{0.4} = \frac{9.36 \times 10}{0.4 \times 10} = \frac{93.6}{4}.\]

  1. Performing the Division

Now we divide \(93.6\) by \(4\). We can perform this division as follows:

  • \(93 \div 4 = 23\) with a remainder of \(1\).
  • Bring down the decimal part \(6\) to get \(1.6\).
  • \(1.6 \div 4 = 0.4\).

Combining these results, we get \(23 + 0.4 = 23.4\).
Alternatively, we can express the operation as:
\[\frac{93.6}{4} = \frac{92 + 1.6}{4} = \frac{92}{4} + \frac{1.6}{4} = 23 + 0.4 = 23.4.\]

  1. Conclusion

The quotient of \(9.36\) and \(0.4\) is \(23.4\). Thus, \(\boxed{23.4}\).

Examples

Dividing decimals is frequently used when managing personal finances or shopping. For instance, if you purchase a package of bulk items costing R\$9.36 and each unit costs R\$0.40, you can determine how many units are in the package by calculating \(9.36 \div 0.4 = 23.4\). This skill helps you verify unit pricing and ensure you are getting the correct quantity for the price paid.

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