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
529
5.29 times 10 squared
52.9
5.29 times 10 Superscript 1
5.29
5.29 times 10 Superscript 0
0.529
5.29 times 10 Superscript negative 1
0.0529
5.29 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 decreases, the number increases.
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 increases, the number decreases.
Number
Powers of 10
529
5.29 times 10 squared
52.9
5.29 times 10 Superscript 1
5.29
5.29 times 10 Superscript 0
0.529
5.29 times 10 Superscript negative 1
0.0529
5.29 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 decreases, the number increases.
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 increases, the number decreases.
Answers
GPT-4o mini
To find the pattern between the number and the powers of 10 as presented in your examples, we can analyze how the position of the decimal point changes with each exponent of 10.
Here’s how the numbers relate to the powers of 10:
1. **529** can be expressed as \(5.29 \times 10^2\).
2. **52.9** can be expressed as \(5.29 \times 10^1\).
3. **5.29** can be expressed as \(5.29 \times 10^0\).
4. **0.529** can be expressed as \(5.29 \times 10^{-1}\).
5. **0.0529** can be expressed as \(5.29 \times 10^{-2}\).
Now let's observe the pattern with respect to the exponents:
- When the exponent increases by 1 (e.g., from \(10^{-2}\) to \(10^{-1}\)), the decimal point moves to the right.
- When the exponent decreases by 1 (e.g., from \(10^0\) to \(10^{-1}\)), the decimal point moves to the left.
### Observations:
- As the exponent of 10 increases (from the negatives to zero and to positive), the value of the overall number also increases.
- As the exponent of 10 decreases (moving from positive to negative), the overall number decreases.
### Analyzing the Choices:
A. **As the exponent of 10 decreases, the number increases.**
- This is false because as the exponent of 10 decreases (from positive to negative), the number actually decreases.
B. **As the exponent of 10 increases, the number increases.**
- This is true because as the exponent of 10 increases from negative numbers to positive numbers, the value of the number indeed increases.
C. **When the exponent of 10 is negative, the number is greater than 1.**
- This is false because when the exponent is negative (e.g., \(-1\) and \(-2\)), the number is less than 1.
D. **As the exponent of 10 increases, the number decreases.**
- This is false; as the exponent increases, the number increases.
### Conclusion:
The correct pattern is: **B. As the exponent of 10 increases, the number increases.**
Here’s how the numbers relate to the powers of 10:
1. **529** can be expressed as \(5.29 \times 10^2\).
2. **52.9** can be expressed as \(5.29 \times 10^1\).
3. **5.29** can be expressed as \(5.29 \times 10^0\).
4. **0.529** can be expressed as \(5.29 \times 10^{-1}\).
5. **0.0529** can be expressed as \(5.29 \times 10^{-2}\).
Now let's observe the pattern with respect to the exponents:
- When the exponent increases by 1 (e.g., from \(10^{-2}\) to \(10^{-1}\)), the decimal point moves to the right.
- When the exponent decreases by 1 (e.g., from \(10^0\) to \(10^{-1}\)), the decimal point moves to the left.
### Observations:
- As the exponent of 10 increases (from the negatives to zero and to positive), the value of the overall number also increases.
- As the exponent of 10 decreases (moving from positive to negative), the overall number decreases.
### Analyzing the Choices:
A. **As the exponent of 10 decreases, the number increases.**
- This is false because as the exponent of 10 decreases (from positive to negative), the number actually decreases.
B. **As the exponent of 10 increases, the number increases.**
- This is true because as the exponent of 10 increases from negative numbers to positive numbers, the value of the number indeed increases.
C. **When the exponent of 10 is negative, the number is greater than 1.**
- This is false because when the exponent is negative (e.g., \(-1\) and \(-2\)), the number is less than 1.
D. **As the exponent of 10 increases, the number decreases.**
- This is false; as the exponent increases, the number increases.
### Conclusion:
The correct pattern is: **B. As the exponent of 10 increases, the number increases.**