Question
Find a pattern between the number and the powers of 10. Use pencil and paper. Explain how the position of the decimal point in each number changes as the exponent in the power of 10 increases or decreases.
Number
Powers of 10
621
6.21 times 10 squared
62.1
6.21 times 10 Superscript 1
6.21
6.21 times 10 Superscript 0
0.621
6.21 times 10 Superscript negative 1
0.0621
6.21 times 10 Superscript negative 2
.
.
.
Question content area right
Part 1
Which of the following is a pattern between the number and the power of 10?
A.
As the exponent of 10 increases, the number decreases.
B.
As the exponent of 10 increases, the number increases.
C.
When the exponent of 10 is negative, the number is greater than 1.
D.
As the exponent of 10 decreases, the number increases.
Number
Powers of 10
621
6.21 times 10 squared
62.1
6.21 times 10 Superscript 1
6.21
6.21 times 10 Superscript 0
0.621
6.21 times 10 Superscript negative 1
0.0621
6.21 times 10 Superscript negative 2
.
.
.
Question content area right
Part 1
Which of the following is a pattern between the number and the power of 10?
A.
As the exponent of 10 increases, the number decreases.
B.
As the exponent of 10 increases, the number increases.
C.
When the exponent of 10 is negative, the number is greater than 1.
D.
As the exponent of 10 decreases, the number increases.
Answers
GPT-4o mini
To analyze the pattern between the number and the powers of 10 you've provided, we can observe how the decimal point moves with respect to the exponent.
### Given Data
- **621** = \(6.21 \times 10^2\)
- **62.1** = \(6.21 \times 10^1\)
- **6.21** = \(6.21 \times 10^0\)
- **0.621** = \(6.21 \times 10^{-1}\)
- **0.0621** = \(6.21 \times 10^{-2}\)
### Observation
1. When the exponent of 10 **increases** (from \(10^{-2}\) to \(10^2\)):
- The number increases from **0.0621** to **621**.
- The decimal point moves **to the right**.
2. When the exponent of 10 **decreases** (from \(10^2\) to \(10^{-2}\)):
- The number decreases from **621** to **0.0621**.
- The decimal point moves **to the left**.
### Results
- The movement of the decimal point:
- Each increase in the exponent by 1 results in the decimal point moving **one place to the right**.
- Each decrease in the exponent by 1 results in the decimal point moving **one place to the left**.
### Conclusion
The correct pattern between the number and the power of 10 is:
- **B. As the exponent of 10 increases, the number increases.**
This is because as the exponent grows, the value represented by the coefficient (6.21) multiplied by the increasing power of 10 yields larger numbers. Conversely, decreasing the exponent results in smaller numbers.
### Given Data
- **621** = \(6.21 \times 10^2\)
- **62.1** = \(6.21 \times 10^1\)
- **6.21** = \(6.21 \times 10^0\)
- **0.621** = \(6.21 \times 10^{-1}\)
- **0.0621** = \(6.21 \times 10^{-2}\)
### Observation
1. When the exponent of 10 **increases** (from \(10^{-2}\) to \(10^2\)):
- The number increases from **0.0621** to **621**.
- The decimal point moves **to the right**.
2. When the exponent of 10 **decreases** (from \(10^2\) to \(10^{-2}\)):
- The number decreases from **621** to **0.0621**.
- The decimal point moves **to the left**.
### Results
- The movement of the decimal point:
- Each increase in the exponent by 1 results in the decimal point moving **one place to the right**.
- Each decrease in the exponent by 1 results in the decimal point moving **one place to the left**.
### Conclusion
The correct pattern between the number and the power of 10 is:
- **B. As the exponent of 10 increases, the number increases.**
This is because as the exponent grows, the value represented by the coefficient (6.21) multiplied by the increasing power of 10 yields larger numbers. Conversely, decreasing the exponent results in smaller numbers.