Convert the following number into correct scientific notation.
[tex]$\begin{array}{c}
94 \times 10^3 \\
{[?] \times 10^{[?]}}
\end{array}$[/tex]
Enter the coefficient in the green box and the exponent in the yellow box.
Answer (1)
Rewrite 94 as 9.4 × 1 0 1 .
Substitute this into the original expression: 94 × 1 0 3 = ( 9.4 × 1 0 1 ) × 1 0 3 .
Use the property of exponents to simplify: 9.4 × ( 1 0 1 × 1 0 3 ) = 9.4 × 1 0 1 + 3 = 9.4 × 1 0 4 .
The number in scientific notation is 9.4 × 1 0 4 .
Explanation
Understanding Scientific Notation We are given the number 94 \t × 1 0 3 and we want to express it in scientific notation. Scientific notation requires the number to be in the form a \t × 1 0 b , where 1 \t ≤ a < 10 and b is an integer.
Rewriting the Coefficient First, we rewrite 94 as 9.4 \t × 1 0 1 .
Substituting Back Now, substitute this back into the original expression: 94 \t × 1 0 3 = ( 9.4 \t × 1 0 1 ) \t × 1 0 3 .
Simplifying the Expression Using the property of exponents a m \t × a n = a m + n , we simplify the expression: 9.4 \t × ( 1 0 1 \t × 1 0 3 ) = 9.4 \t × 1 0 1 + 3 = 9.4 \t × 1 0 4 .
Final Answer Therefore, the number in scientific notation is 9.4 \t × 1 0 4 .
Examples
Scientific notation is used in many fields, such as physics, astronomy, and chemistry, to represent very large or very small numbers. For example, the distance to the sun is approximately 1.5 × 1 0 11 meters, 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 total mass of 6.022 × 1 0 23 (Avogadro's number) hydrogen atoms, each with a mass of approximately 1.67 × 1 0 − 27 kg. Scientific notation simplifies this calculation and prevents errors from writing out many zeros.
