Question
A news podcast has 77,000 subscribers. Write an estimate for the number of subscribers as a single digit times an integer power of 10 . Show your work.
Ask by Henry Bartlett. in the United States
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
77,000 is approximately \(8 \times 10^4\).
Solution
To express **77,000** subscribers as a single digit multiplied by an integer power of 10, follow these steps:
1. **Identify the Appropriate Power of 10:**
Determine the power of 10 that is closest to 77,000.
- \(10^4 = 10,000\)
- \(10^5 = 100,000\)
77,000 lies between \(10^4\) and \(10^5\).
2. **Determine the Single Digit:**
Since 77,000 is closer to 100,000 than to 10,000, we'll use \(10^4\) as the base.
- \( \frac{77,000}{10,000} = 7.7 \)
Round 7.7 to the nearest single digit, which is **8**.
3. **Combine the Single Digit with the Power of 10:**
- **Estimate:** \(8 \times 10^4\)
4. **Verification:**
- \(8 \times 10^4 = 80,000\)
This estimate is close to the actual number of subscribers (77,000).
**Final Estimate:**
\[
77,\!000 \approx 8 \times 10^4
\]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Extra Insights
To express 77,000 as a single digit times an integer power of 10, we can break it down as follows: 1. Count the number of digits in 77,000: it has 5 digits. 2. To represent it as a single digit, we can identify the leading significant figure, which is 7. 3. Now, we express the remaining part (77,000 = 7.7 * 10^4) to get it in proper format. 4. The correct formatting gives us 7.7 as the single digit. However, to adhere strictly to the format of a single digit times a power of 10, it would be simplified to: 77,000 ≈ 7.7 × 10^4 ≈ 8 × 10^4 (if we round) Thus, the estimated form is: 7.7 × 10^4 or simply 8 × 10^4 as an approximate representation.
