Verified Answer :

  • Recognize the operation as division by 100.
  • Apply the rule for division by powers of 10: move the decimal point two places to the left.
  • Perform the shift on the value -12.405.
  • The final result is \(\boxed{-0.12405}\).

Explanation

  1. Analysis of the Problem

We are given the expression \(\frac{-12.405}{100}\). This is a division problem where we need to divide a decimal number, -12.405, by the power of 10, specifically 100. The objective is to find the resulting decimal value.

  1. Method for Division by 100

Dividing a decimal number by a power of 10, such as 10, 100, or 1000, can be easily accomplished by shifting the decimal point to the left. For each zero in the power of 10 divisor, the decimal point moves one position to the left. Since 100 has two zeros, we must move the decimal point in -12.405 two places to the left.

  1. Execution of the Calculation

Starting with the number -12.405, we move the decimal point two places to the left:

  1. Moving one place left: -1.2405
  2. Moving the second place left: -0.12405

Thus, \(-12.405 \div 100 = -0.12405\).

  1. Conclusion and Final Answer

The final result of dividing -12.405 by 100 is \(-0.12405\). Therefore, \(\frac{-12.405}{100} = \boxed{-0.12405}\).

Examples

In everyday life, dividing by powers of 10 is common when performing unit conversions. For example, if you have a measurement in centimeters, such as 12.405 cm, and you want to convert it to meters, you divide by 100 (since 100 cm = 1 m). This results in 0.12405 meters, illustrating how moving the decimal point helps scale values quickly and accurately.

Related Questions