High School

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Which symbol would you use to correctly compare the following numbers? Draw a number line to help you.

6.2 × 10⁻³, 0, and 1

A. 0 < 6.2 × 10⁻³ < 1
B. 6.2 × 10⁻³ < 0 and 6.2 × 10⁻³ > 1
C. 6.2 × 10⁻³ > 0 and 6.2 × 10⁻³ > 1
D. 6.2 × 10⁻³ < 0 and 6.2 × 10⁻³ < 1

Answer :

Final answer:

The correct comparison of the numbers is (option 1.) 0 < 6.2 X 10^{-3} < 1. This is visualized on a number line where 0.0062 (6.2 X 10^{-3}) is positioned between 0 and 1.

Explanation:

To compare the numbers 6.2 X 10^{-3}, 0, and 1, we first need to understand what 6.2 X 10^{-3} represents in decimal form. The expression 6.2 X 10^{-3} means that the decimal point in 6.2 is moved three places to the left, which gives us 0.0062.

According to the properties of numbers, any positive number is greater than 0. Therefore, 6.2 X 10^{-3} is greater than 0. Now, since 0.0062 is less than 1, the correct comparison is 0 < 6.2X 10^{-3} < 1.

To visualize this, you can draw a number line:

  • Mark a point for 0.
  • Mark a point to the right of 0 for 6.2 X 10^{-3} which is equivalent to 0.0062.
  • Mark another point further to the right for 1.

This visually confirms that 0.0062 lies between 0 and 1 on the number line.

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