Let's work through the questions in the image you uploaded.

31–35: Express in Decimal and Exponential Notation

Here are the decimal and exponential representations:

31. $\frac{1}{10} = 0.1 = 1.0 \times 10^{-1}$
32. $\frac{1}{100} = 0.01 = 1.0 \times 10^{-2}$
33. $\frac{1}{1000} = 0.001 = 1.0 \times 10^{-3}$
34. $\frac{1}{1,000,000} = 0.000001 = 1.0 \times 10^{-6}$
35. $\frac{1}{10,000} = 0.0001 = 1.0 \times 10^{-4}$

36–40: Logarithms of Numbers

Here are the logarithmic values:

36. $100 = 10^2$, so $\log_{10} 100 = 2$
37. $10 = 10^1$, so $\log_{10} 10 = 1$
38. $1 = 10^0$, so $\log_{10} 1 = 0$
39. $0.1 = 10^{-1}$, so $\log_{10} 0.1 = -1$
40. $0.01 = 10^{-2}$, so $\log_{10} 0.01 = -2$

Would you like a detailed explanation of any of these? Let me know if you have any further questions.

Here are 5 related questions for further practice:

1. What is $\frac{1}{1,000,000,000}$ in decimal and exponential form?
2. What is the logarithm of $1000$?
3. How do you express $\frac{1}{100,000}$ in both decimal and exponential notation?
4. What is the value of $\log_{10} 0.001$?
5. What does $\log_{10} 10,000$ equal?

Tip: For logarithms, remember that $\log_{10}$ (log base 10) of a number tells you the exponent to which 10 must be raised to get that number.