How do you figure out how to express the mass of the electron to significant figures?

Do you mean to two s.f.? or something different?

My text lists the mass of the electron as

My text lists the mass of the electron as 9.10940 x 10^-31 kg. To two s.f. that is

9.1 x 10^-31 kg.

To express the mass of the electron to significant figures, you need to follow a few steps:

1. Start with the known value for the mass of the electron. According to the International System of Units (SI), the mass of an electron is approximately 9.10938356 × 10^-31 kilograms.

2. Determine the number of significant figures in the known value. In this case, the known value has 11 significant figures.

3. Identify the desired number of significant figures for the answer. For example, if you want to express the mass of the electron to 3 significant figures, the desired number is 3.

4. Round the known value to the desired number of significant figures. To do this, count digits from the left until you reach the desired number. If the digit following the desired number is 5 or greater, round up; if it is less than 5, round down. Replace all the digits to the right of the desired number with zeros.

For example, if you want to express the mass of the electron to 3 significant figures:
9.10938356 × 10^-31 kilograms becomes 9.11 × 10^-31 kilograms.

Remember that rounding affects the value, so it's important to consider the desired level of accuracy and the significance of the measurement in the context you are working with.