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The miles of track in the U.S. railroad system peaked in the early $1900$ s. At that time, more than $270,000$ miles of track crisscrossed the country. What is the approximate amount of track written in scientific notation? $\newline$ Choices: $\newline$ (A) $3 \times 10^4$ miles $\newline$ (B) $3 \times 10^5$ miles $\newline$ (C) $3 \times 10^6$ miles $\newline$ (D) $3 \times 10^7$ miles

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Volume of cubes and rectangular prisms: word problems

Full solution

Q. The miles of track in the U.S. railroad system peaked in the early

1900

s. At that time, more than

270,000

miles of track crisscrossed the country. What is the approximate amount of track written in scientific notation?

\newline

Choices:

\newline

(A)

3 \times 10^4

miles

\newline

(B)

3 \times 10^5

miles

\newline

(C)

3 \times 10^6

miles

\newline

(D)

3 \times 10^7

miles

Identify track length: We got $270,000$ miles of track. To write this in scientific notation, we need to express it as a number between $1$ and $10$ multiplied by a power of $10$ .
Move decimal point: Move the decimal point in $270,000$ so it's after the first non-zero digit. That's $2.7$ . Now count how many places we moved the decimal. That's $5$ places.
Express in scientific notation: So, $270,000$ is $2.7$ times $10$ to the power of $5$ , but we need it to be a number times $10$ , so we round $2.7$ to $3$ to match the choices given.

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