- Identify the given values in the scientific notation \(a \times 10^n\) as \(a=2.4\) and \(n=-4\).
- Understand that a negative exponent \(n=-4\) indicates shifting the decimal point 4 places to the left.
- Perform the conversion by moving the decimal point: \(2.4 \to 0.24 \to 0.024 \to 0.0024 \to 0.00024\).
- The final standard notation is \(\boxed{0.00024}\).
Explanation
- Analysis of Scientific Notation
The expression provided is in scientific notation, which is a method used to write very large or very small numbers compactly. The form is given by \(a \times 10^n\), where \(1 \le |a| < 10\) and \(n\) is an integer. In the given expression \(2.4 \times 10^{-4}\), we identify that \(a = 2.4\) and the exponent \(n = -4\). The negative exponent signifies that the number is less than 1, and specifically, the decimal point in 2.4 must be shifted to the left by 4 places to convert it into standard decimal notation.
- Conversion to Standard Notation
To convert \(2.4 \times 10^{-4}\) to standard decimal notation, we start with the number 2.4 and move the decimal point 4 places to the left.
- Moving the decimal point 1 place to the left gives \(0.24\).
- Moving it 2 places to the left gives \(0.024\).
- Moving it 3 places to the left gives \(0.0024\).
- Moving it 4 places to the left gives \(0.00024\).
Alternatively, we can think of this as multiplying 2.4 by \(10^{-4} = 0.0001\), which results in \(0.00024\).
- Conclusion
After shifting the decimal point 4 places to the left from its original position between 2 and 4, we arrive at the standard decimal value. The final result is 0.00024. Therefore, the value of the expression is \(\boxed{0.00024}\).
Examples
Scientific notation is widely used in fields like physics and chemistry to represent extremely small or large quantities, such as the mass of an atom or the distance between stars. For instance, if a scientist measures the thickness of a microscopic film to be \(2.4 \times 10^{-4}\) meters, converting this to standard notation as \(0.00024\) meters helps in understanding the actual scale of the measurement in everyday units. This practice is essential for comparing values and performing calculations efficiently in technical environments.