Verified Answer :

  • Multiply the given value \(0.00815\) by \(10^{-2}\).
  • Interpret multiplying by \(10^{-2}\) as moving the decimal point two positions to the left.
  • Perform the shift: \(0.00815 \rightarrow 0.000815 \rightarrow 0.0000815\).
  • Conclude that the result is \(\boxed{0.0000815}\).

Explanation

  1. Understanding the Operation

To evaluate the expression \(0.00815 \times 10^{-2}\), we need to understand the effect of multiplying a decimal number by a negative power of ten. The expression \(10^{-2}\) is equivalent to \(\frac{1}{10^2}\), which is \(\frac{1}{100}\), or \(0.01\). Multiplying any decimal number by \(10^{-n}\) is equivalent to moving its decimal point \(n\) places to the left. In this case, we have \(n = 2\), so we need to move the decimal point of \(0.00815\) two places to the left.

  1. Calculating the Result

We start with the number \(0.00815\). To multiply this by \(10^{-2}\), we move the decimal point two places to the left:

  1. Moving it one place left gives \(0.000815\).
  2. Moving it one more place left gives \(0.0000815\).

Thus, \(0.00815 \times 10^{-2} = 0.0000815\). Comparing this result with the given options, it clearly matches the third option in the list.

Examples

This type of calculation is very important in fields like science and engineering when dealing with scientific notation and extremely small measurements. For example, if a measurement of a microchip component is given as \(0.00815\) millimeters, and you need to convert it into a unit that is a hundred times smaller, you would perform exactly this operation to find the new value in the required units. Mastering this shift helps in scaling data accurately and maintaining precision in calculations.

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