To express the number 75,200 in scientific notation, we aim to write it in the form [tex]\( a \times 10^b \)[/tex], where [tex]\( 1 \leq a < 10 \)[/tex] and [tex]\( b \)[/tex] is an integer. Let's go through the steps to find the power of 10 for this number.
1. Identify the significant figure part (a):
We need to convert 75,200 into a number between 1 and 10 multiplied by a power of 10. For 75,200, we need to move the decimal point to make it between 1 and 10:
[tex]\[
75,200 \rightarrow 7.52
\][/tex]
2. Count how many places the decimal has moved (b):
Originally, the decimal point in 75,200 is at the end of the number. To convert 75,200 to 7.52, we move the decimal point 4 places to the left:
[tex]\[
75,200 \rightarrow 7.5200 \rightarrow 7.52 \times 10^4
\][/tex]
3. Determine the power of 10:
The number of places we moved the decimal point gives us the exponent. In this case, we moved 4 places to the left. Therefore, the power of 10 (b) is 4.
So, when we write 75,200 in scientific notation, it is:
[tex]\[
75,200 = 7.52 \times 10^4
\][/tex]
Thus, the power of 10 when 75,200 is written in scientific notation is:
[tex]\[
\boxed{4}
\][/tex]
