Convert the following number into correct scientific notation.
[tex]$\begin{array}{c}
20 \times 10^4 \
{[?] \times 10^{[?]}}
\end{array}$[/tex]
Enter the coefficient in the green box and the exponent in the yellow box.
Coefficient
[$\square$]
Exponent
[$\square$]
Answer (2)
The correct scientific notation for the number 20 × 1 0 4 is 2 × 1 0 5 . The coefficient is 2 and the exponent is 5. Therefore, fill in the green box with 2 and the yellow box with 5.
;
Rewrite 20 as 2 × 1 0 1 .
Substitute into the original expression: ( 2 × 1 0 1 ) × 1 0 4 .
Use the property of exponents to simplify: 2 × 1 0 1 + 4 .
Calculate the exponent: 2 × 1 0 5 . The coefficient is 2 and the exponent is 5. 2 × 1 0 5
Explanation
Understanding Scientific Notation We are given the number 20 × 1 0 4 and asked to convert it into 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.
Rewriting the Coefficient First, we can rewrite 20 as 2 × 1 0 1 . So, the given number can be written as ( 2 × 1 0 1 ) × 1 0 4 .
Applying Exponent Rules Next, we use the property of exponents that states a m × a n = a m + n . Applying this property, we have 2 × ( 1 0 1 × 1 0 4 ) = 2 × 1 0 1 + 4 .
Simplifying the Exponent Now, we simplify the exponent: 1 + 4 = 5 . Therefore, the number in scientific notation is 2 × 1 0 5 .
Final Answer The coefficient is 2 and the exponent is 5.
Examples
Scientific notation is used in many fields, such as physics and astronomy, 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.
