Question

Order the numbers from smallest to largest. Use the number line as a guide to ensure you put the numbers in the correct order.

(6 points)

(smallest number) _____, _____, _____, _____, _____, (largest number)

−7.6×10
−9

3.2×10
4

9.3×10
−7

4.5×10
4

5.7×10
13

1.9×10
7

Answer 1

To order the numbers from smallest to largest, we first need to evaluate each of the scientific notation numbers. Here are the numbers written out:

1. \(-7.6 \times 10^{-9}\) = \(-0.0000000076\)
2. \(3.2 \times 10^{4}\) = \(32000\)
3. \(9.3 \times 10^{-7}\) = \(0.00000093\)
4. \(4.5 \times 10^{4}\) = \(45000\)
5. \(5.7 \times 10^{13}\) = \(57000000000000\)
6. \(1.9 \times 10^{7}\) = \(19000000\)

Now, let's compare these values to determine their order:

- \(-7.6 \times 10^{-9}\) is the smallest,
- \(9.3 \times 10^{-7}\) is next (still negative but closer to zero),
- \(3.2 \times 10^{4}\) is \(32000\),
- \(4.5 \times 10^{4}\) is \(45000\),
- \(1.9 \times 10^{7}\) is \(19000000\),
- \(5.7 \times 10^{13}\) is the largest.

Putting these in order from smallest to largest, we have:

\(-7.6 \times 10^{-9}\), \(9.3 \times 10^{-7}\), \(3.2 \times 10^{4}\), \(4.5 \times 10^{4}\), \(1.9 \times 10^{7}\), \(5.7 \times 10^{13}\)

So, the final ordered list is:

(smallest number) \(-7.6 \times 10^{-9}\), \(9.3 \times 10^{-7}\), \(3.2 \times 10^{4}\), \(4.5 \times 10^{4}\), \(1.9 \times 10^{7}\), (largest number) \(5.7 \times 10^{13}\)