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.
-10-9-8-7-6-5-4-3-2-10 1 2 3 4 5 6 7 8 9 10
Item 1
Item 2
Item 3
Item 4
Item 5
Item 6
(6 points)
(smallest number)
<
(largest number)
25.7 * 10 ^ 13
= 1.9 * 10 ^ 7
7 * 9.3 * 10 ^ - 7
:: 4.5 * 10 ^ 4
: - 7.6 * 10 ^ - 9
= 3.2 * 10 ^ 4

Answer 1

To order the given numbers from smallest to largest, we first need to convert them into a comparable format. Here are the numbers you've provided:

1. \( 25.7 \times 10^{13} \)
2. \( 1.9 \times 10^{7} \)
3. \( 7 \times 9.3 \times 10^{-7} \) (which can be calculated to be \( 6.51 \times 10^{-6} \))
4. \( 4.5 \times 10^{4} \)
5. \( -7.6 \times 10^{-9} \)
6. \( 3.2 \times 10^{4} \)

Now, we will convert all of the numbers into standard decimal form for easier comparison:

1. \( 25.7 \times 10^{13} = 25700000000000 \)
2. \( 1.9 \times 10^{7} = 19000000 \)
3. \( 6.51 \times 10^{-6} = 0.00000651 \)
4. \( 4.5 \times 10^{4} = 45000 \)
5. \( -7.6 \times 10^{-9} = -0.0000000076 \)
6. \( 3.2 \times 10^{4} = 32000 \)

Now we can compare these values:

- The smallest number is \( -7.6 \times 10^{-9} \).
- The next number is \( 6.51 \times 10^{-6} \) (or \( 7 \times 9.3 \times 10^{-7} \)).
- After that is \( 3.2 \times 10^{4} = 32000 \).
- Then \( 4.5 \times 10^{4} = 45000 \).
- Next is \( 1.9 \times 10^{7} = 19000000 \).
- Finally, the largest number is \( 25.7 \times 10^{13} = 25700000000000 \).

So the ordered list from smallest to largest is:

1. \( -7.6 \times 10^{-9} \)
2. \( 6.51 \times 10^{-6} \)
3. \( 3.2 \times 10^{4} \)
4. \( 4.5 \times 10^{4} \)
5. \( 1.9 \times 10^{7} \)
6. \( 25.7 \times 10^{13} \)

In conclusion, here are the items in order:

1. \( -7.6 \times 10^{-9} \)
2. \( 7 \times 9.3 \times 10^{-7} \)
3. \( 3.2 \times 10^{4} \)
4. \( 4.5 \times 10^{4} \)
5. \( 1.9 \times 10^{7} \)
6. \( 25.7 \times 10^{13} \)

This gives you a clear and correct sequence from smallest to largest.