Write the value of the underlined digit.

Here are the solutions to the problems:

Write the value of the underlined digit.

3. In 0.418, the '4' is in the tenths place.
The value is $\boxed{\mathbf{0.4}}$.

4. In 5.296, the '9' is in the hundredths place.
The value is $\boxed{\mathbf{0.09}}$.

5. In 3.806, the '0' is in the hundredths place.
The value is $\boxed{\mathbf{0.00}}$.

6. In 0.547, the '7' is in the thousandths place.
The value is $\boxed{\mathbf{0.007}}$.

7. In 1.96, the '6' is in the hundredths place.
The value is $\boxed{\mathbf{0.06}}$.

8. In 0.869, the '6' is in the hundredths place.
The value is $\boxed{\mathbf{0.06}}$.

9. In 20.5, the '5' is in the tenths place.
The value is $\boxed{\mathbf{0.5}}$.

10. In 14.234, the '2' is in the tenths place.
The value is $\boxed{\mathbf{0.2}}$.

Write the number in two other forms.

11. Standard form: 0.125
Word form: One hundred twenty-five thousandths
Expanded form:

$$0.1 + 0.02 + 0.005$$

12. Expanded form: $4 + 0.9 + 0.008$
Standard form: $\boxed{\mathbf{4.908}}$
Word form: Four and nine hundred eight thousandths

13. A gopher tortoise weighs eleven and thirty-two thousandths pounds.
Standard form: $\boxed{\mathbf{11.032}}$

14. Construct an Argument: Is 9.540 equivalent to 9.54? Explain.
Yes, they are equivalent. Adding a zero at the end of a decimal number, after the last non-zero digit, does not change its value.

15. DIG DEEPER: Write three decimals that are equivalent to $6 \times 1 + 4 \times \frac{1}{10}$.
First, calculate the value:

$$6 \times 1 + 4 \times \frac{1}{10} = 6 + 0.4 = 6.4$$

Three equivalent decimals are: $\boxed{\mathbf{6.40}}$, $\boxed{\mathbf{6.400}}$, $\boxed{\mathbf{6.4000}}$.