To write the number 322,000,000 in scientific notation, follow these steps:
1. Identify the Significant Figures: The goal is to express the number in the form [tex]\( a \times 10^n \)[/tex], where [tex]\( 1 \leq a < 10 \)[/tex] and [tex]\( n \)[/tex] is an integer.
2. Normalize the Number: Move the decimal point in the number 322,000,000 so that there's only one non-zero digit to the left of the decimal point. In this case, moving the decimal point 8 places to the left gives:
[tex]\[
3.22
\][/tex]
3. Count the Decimal Moves: Since we moved the decimal point 8 places to the left, we need to multiply by [tex]\( 10^8 \)[/tex] to get back to the original value.
4. Construct the Scientific Notation: Combine the normalized number with the power of 10 to get:
[tex]\[
3.22 \times 10^8
\][/tex]
So, the number 322,000,000 written in scientific notation is:
[tex]\[
3.22 \times 10^8
\][/tex]
Hence, the correct answer from the provided options is:
[tex]\[
3.22 \times 10^8
\][/tex]
