The U.S. population in $1970$ was $203,211,926$ . What was the approximate population written in scientific notation? $\newline$ Choices: $\newline$ (A) $2 \times 10^7$ $\newline$ (B) $2 \times 10^8$ $\newline$ (C) $2 \times 10^9$ $\newline$ (D) $2 \times 10^{10}$

Full solution

Q. The U.S. population in

1970

was

203,211,926

. What was the approximate population written in scientific notation?

\newline

Choices:

\newline

(A)

2 \times 10^7

\newline

(B)

2 \times 10^8

\newline

(C)

2 \times 10^9

\newline

(D)

2 \times 10^{10}

Identify significant digits: First, let's identify the most significant digits of the population number. We have $203,211,926$ which starts with $203$ . We want to turn this into a number between $1$ and $10$ for scientific notation.
Move decimal point: Now, we move the decimal point in $203$ so that it's after the first digit, which gives us $2.03211926$ . We moved the decimal point $2$ places to the left.
Count decimal places moved: Count how many places we moved the decimal point to get from $203,211,926$ to $2.03211926$ . We moved it $8$ places.
Write in scientific notation: Write the number in scientific notation as $2.03211926 \times 10$ to the power of the number of places we moved the decimal point, which is $8$ . So, it's $2.03211926 \times 10^8$ .
Round to approximate value: Since we need an approximate value and the choices are all in the form of $2 \times 10^x$ , we can round $2.03211926$ to $2$ . This gives us $2 \times 10^8$ .
Find correct answer: Look at the choices to find our answer. The correct scientific notation that matches our calculation is $(B)2 \times 10^8$ .