Express the following in correct scientific notation:
[tex]$\begin{array}{c}
94 \times 10^3 \
{[?] \times 10^{[?]}}
\end{array}$[/tex]
Enter the coefficient and the exponent.
Answer (2)
Rewrite 94 × 1 0 3 as 9.4 × 1 0 1 × 1 0 3 .
Simplify using exponent rules: 9.4 × 1 0 1 + 3 .
Calculate the exponent: 1 + 3 = 4 .
The final scientific notation is 9.4 × 1 0 4 .
Explanation
Understanding Scientific Notation We are given the number 94 × 1 0 3 and asked to express it in correct scientific notation. Scientific notation requires the number to be in the form a × 1 0 b , where 1 ≤ a < 10 and b is an integer.
Adjusting the Coefficient To convert 94 × 1 0 3 into scientific notation, we need to adjust the coefficient 94 so that it falls between 1 and 10. We can do this by dividing 94 by 10 to get 9.4. Since we divided the coefficient by 10, we must multiply the power of 10 by 10 to keep the number the same.
Applying Exponent Rules So, we rewrite 94 × 1 0 3 as 9.4 × 10 × 1 0 3 . Using the property of exponents that a m × a n = a m + n , we can simplify this to 9.4 × 1 0 1 + 3 .
Calculating the Exponent Now, we calculate the exponent: 1 + 3 = 4 . Therefore, the number in scientific notation is 9.4 × 1 0 4 .
Final Answer The number 94 × 1 0 3 expressed in scientific notation is 9.4 × 1 0 4 .
Examples
Scientific notation is used in many fields, such as physics, astronomy, and engineering, to represent very large or very small numbers. For example, the speed of light is approximately 3 × 1 0 8 meters per second, and the mass of an electron is approximately 9.11 × 1 0 − 31 kilograms. Using scientific notation makes it easier to work with these numbers and compare their magnitudes. Imagine calculating the distance light travels in a year; expressing both the speed of light and the time in seconds in scientific notation simplifies the multiplication and makes the result more manageable.
The number 94 × 1 0 3 expressed in scientific notation is 9.4 × 1 0 4 , with a coefficient of 9.4 and an exponent of 4.
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