Question: 8. The longest wavelength of visible light is associated with red. It is approximately 0.00000062 meter. What is the value of the exponent when this number is written in scientific notation?
9. An inequality is shown.
$$\frac{11}{100} < x < \frac{\pi}{23}$$
The table lists possible values of $x$. Which values of $x$ would make the inequality true?
Select the correct answer in each row.
Value True False
15.7%
$\frac{3}{25}$
0.1333
$\frac{\sqrt{3}}{10}$
1. **Problem 8:** Find the exponent in the scientific notation of the wavelength $0.00000062$ meters.
2. To write a number in scientific notation, express it as $$a \times 10^n$$ where $1 \leq a < 10$ and $n$ is an integer.
3. Move the decimal point in $0.00000062$ to the right until only one non-zero digit remains to the left:
$$0.00000062 = 6.2 \times 10^{-7}$$
4. The exponent is $-7$.
5. **Problem 9:** Given the inequality $$\frac{11}{100} < x < \frac{\pi}{23}$$, determine which values satisfy it.
6. Calculate approximate decimal values:
$$\frac{11}{100} = 0.11$$
$$\frac{\pi}{23} \approx \frac{3.1416}{23} \approx 0.1366$$
7. Check each value:
- $15.7\% = 0.157$ which is not less than $0.1366$, so **False**.
- $\frac{3}{25} = 0.12$ which lies between $0.11$ and $0.1366$, so **True**.
- $0.1333$ lies between $0.11$ and $0.1366$, so **True**.
- $\frac{\sqrt{3}}{10} \approx \frac{1.732}{10} = 0.1732$ which is greater than $0.1366$, so **False**.
**Final answers:**
- Exponent for wavelength scientific notation: $-7$
- Values satisfying inequality: $\frac{3}{25}$ and $0.1333$ are True; $15.7\%$ and $\frac{\sqrt{3}}{10}$ are False.