Question

3 the population of the state of california was about 37,250,000 people in 2013. which number best approximates the population as a single digit times a power of 10? a ( 4 \times 10^7 ) b ( 4 \times 10^{-7} ) c ( 3 \times 10^{-6} ) d ( 3 \times 10^4 )

Explanation:

Step1: Recall scientific notation rules

Scientific notation is in the form \(a\times10^{n}\), where \(1\leq|a|\lt10\) and \(n\) is an integer. The population is \(37,250,000\).

Step2: Determine \(a\) and \(n\)

First, move the decimal point to get a number between 1 and 10. For \(37,250,000\), moving the decimal 7 places left gives \(3.725\approx4\) (for approximation). The exponent \(n\) is 7 because we moved the decimal 7 places. So in scientific notation, it is approximately \(4\times10^{7}\).

Answer:

A. \(4\times10^{7}\)