Question
List the following numbers in order from least to greatest. Use pencil and paper. Explain why you would write a list in this way.
9.92 times 10 Superscript negative 4
4.49 times 10 Superscript negative 6
6.5 times 10 Superscript negative 8
3.53 times 10 Superscript negative 6
6 times 10 Superscript negative 7
Question content area bottom
Part 1
Choose the correct answer below.
A.6.5 times 10 Superscript negative 8 Baseline comma 6 times 10 Superscript negative 7 Baseline comma 3.53 times 10 Superscript negative 6 Baseline comma 4.49 times 10 Superscript negative 6 Baseline comma 9.92 times 10 Superscript negative 4
6.5 times 10 Superscript negative 8 Baseline comma 6 times 10 Superscript negative 7 Baseline comma 3.53 times 10 Superscript negative 6 Baseline comma 4.49 times 10 Superscript negative 6 Baseline comma 9.92 times 10 Superscript negative 4
B.3.53 times 10 Superscript negative 6 Baseline comma 4.49 times 10 Superscript negative 6 Baseline comma 6 times 10 Superscript negative 7 Baseline comma 6.5 times 10 Superscript negative 8 Baseline comma 9.92 times 10 Superscript negative 4
3.53 times 10 Superscript negative 6 Baseline comma 4.49 times 10 Superscript negative 6 Baseline comma 6 times 10 Superscript negative 7 Baseline comma 6.5 times 10 Superscript negative 8 Baseline comma 9.92 times 10 Superscript negative 4
C.9.92 times 10 Superscript negative 4 Baseline comma 6.5 times 10 Superscript negative 8 Baseline comma 6 times 10 Superscript negative 7 Baseline comma 4.49 times 10 Superscript negative 6 Baseline comma 3.53 times 10 Superscript negative 6
9.92 times 10 Superscript negative 4 Baseline comma 6.5 times 10 Superscript negative 8 Baseline comma 6 times 10 Superscript negative 7 Baseline comma 4.49 times 10 Superscript negative 6 Baseline comma 3.53 times 10 Superscript negative 6
D.9.92 times 10 Superscript negative 4 Baseline comma 4.49 times 10 Superscript negative 6 Baseline comma 3.53 times 10 Superscript negative 6 Baseline comma 6 times 10 Superscript negative 7 Baseline comma 6.5 times 10 Superscript negative 8
9.92 times 10 Superscript negative 4 Baseline comma 4.49 times 10 Superscript negative 6 Baseline comma 3.53 times 10 Superscript negative 6 Baseline comma 6 times 10 Superscript negative 7 Baseline comma 6.5 times 10 Superscript negative 8
9.92 times 10 Superscript negative 4
4.49 times 10 Superscript negative 6
6.5 times 10 Superscript negative 8
3.53 times 10 Superscript negative 6
6 times 10 Superscript negative 7
Question content area bottom
Part 1
Choose the correct answer below.
A.6.5 times 10 Superscript negative 8 Baseline comma 6 times 10 Superscript negative 7 Baseline comma 3.53 times 10 Superscript negative 6 Baseline comma 4.49 times 10 Superscript negative 6 Baseline comma 9.92 times 10 Superscript negative 4
6.5 times 10 Superscript negative 8 Baseline comma 6 times 10 Superscript negative 7 Baseline comma 3.53 times 10 Superscript negative 6 Baseline comma 4.49 times 10 Superscript negative 6 Baseline comma 9.92 times 10 Superscript negative 4
B.3.53 times 10 Superscript negative 6 Baseline comma 4.49 times 10 Superscript negative 6 Baseline comma 6 times 10 Superscript negative 7 Baseline comma 6.5 times 10 Superscript negative 8 Baseline comma 9.92 times 10 Superscript negative 4
3.53 times 10 Superscript negative 6 Baseline comma 4.49 times 10 Superscript negative 6 Baseline comma 6 times 10 Superscript negative 7 Baseline comma 6.5 times 10 Superscript negative 8 Baseline comma 9.92 times 10 Superscript negative 4
C.9.92 times 10 Superscript negative 4 Baseline comma 6.5 times 10 Superscript negative 8 Baseline comma 6 times 10 Superscript negative 7 Baseline comma 4.49 times 10 Superscript negative 6 Baseline comma 3.53 times 10 Superscript negative 6
9.92 times 10 Superscript negative 4 Baseline comma 6.5 times 10 Superscript negative 8 Baseline comma 6 times 10 Superscript negative 7 Baseline comma 4.49 times 10 Superscript negative 6 Baseline comma 3.53 times 10 Superscript negative 6
D.9.92 times 10 Superscript negative 4 Baseline comma 4.49 times 10 Superscript negative 6 Baseline comma 3.53 times 10 Superscript negative 6 Baseline comma 6 times 10 Superscript negative 7 Baseline comma 6.5 times 10 Superscript negative 8
9.92 times 10 Superscript negative 4 Baseline comma 4.49 times 10 Superscript negative 6 Baseline comma 3.53 times 10 Superscript negative 6 Baseline comma 6 times 10 Superscript negative 7 Baseline comma 6.5 times 10 Superscript negative 8
Answers
GPT-4o mini
To organize the given numbers in scientific notation from least to greatest, we first need to convert them into decimal form or at least compare their scientific notation based on the exponent values. Numbers with a smaller exponent (more negative) are smaller in value.
Here are the numbers and their decimal equivalents:
1. \(9.92 \times 10^{-4} = 0.000992\)
2. \(4.49 \times 10^{-6} = 0.00000449\)
3. \(6.5 \times 10^{-8} = 0.000000065\)
4. \(3.53 \times 10^{-6} = 0.00000353\)
5. \(6 \times 10^{-7} = 0.0000006\)
Now let's look at the values obtained:
- \(6.5 \times 10^{-8} = 0.000000065\)
- \(6 \times 10^{-7} = 0.0000006\)
- \(4.49 \times 10^{-6} = 0.00000449\)
- \(3.53 \times 10^{-6} = 0.00000353\)
- \(9.92 \times 10^{-4} = 0.000992\)
Next, we order the values from least to greatest:
1. \(6.5 \times 10^{-8}\)
2. \(6 \times 10^{-7}\)
3. \(3.53 \times 10^{-6}\)
4. \(4.49 \times 10^{-6}\)
5. \(9.92 \times 10^{-4}\)
Thus, the correct order from least to greatest is:
**A.**
\[6.5 \times 10^{-8}, 6 \times 10^{-7}, 3.53 \times 10^{-6}, 4.49 \times 10^{-6}, 9.92 \times 10^{-4}\]
The reasoning for this order is based on the value of each number. In scientific notation, the number with the smaller exponent will yield a smaller decimal value. We compared each exponent's magnitude and ordered them accordingly.
Here are the numbers and their decimal equivalents:
1. \(9.92 \times 10^{-4} = 0.000992\)
2. \(4.49 \times 10^{-6} = 0.00000449\)
3. \(6.5 \times 10^{-8} = 0.000000065\)
4. \(3.53 \times 10^{-6} = 0.00000353\)
5. \(6 \times 10^{-7} = 0.0000006\)
Now let's look at the values obtained:
- \(6.5 \times 10^{-8} = 0.000000065\)
- \(6 \times 10^{-7} = 0.0000006\)
- \(4.49 \times 10^{-6} = 0.00000449\)
- \(3.53 \times 10^{-6} = 0.00000353\)
- \(9.92 \times 10^{-4} = 0.000992\)
Next, we order the values from least to greatest:
1. \(6.5 \times 10^{-8}\)
2. \(6 \times 10^{-7}\)
3. \(3.53 \times 10^{-6}\)
4. \(4.49 \times 10^{-6}\)
5. \(9.92 \times 10^{-4}\)
Thus, the correct order from least to greatest is:
**A.**
\[6.5 \times 10^{-8}, 6 \times 10^{-7}, 3.53 \times 10^{-6}, 4.49 \times 10^{-6}, 9.92 \times 10^{-4}\]
The reasoning for this order is based on the value of each number. In scientific notation, the number with the smaller exponent will yield a smaller decimal value. We compared each exponent's magnitude and ordered them accordingly.