Chapter 1 - Introduction to Chemistry - Questions and Exercises - Exercises - Page 34: 1.50

(a) 8.20 x 10$^{-3}$ kg (b) 1.01 m (c) 18.998 g (d) 19.00 g

(a) To reduce the number 0.08205 kg to three significant figures, we look at the first three significant figures: 8, 2, and 0. Definitely, we will use the 8 and 2. As for the 0, we look at the digit after it and see that it is a 5; therefore, we round to even to get 0.0820. To express this number better, we can represent it with scientific notation using the three significant digits to get 8.20 x 10$^{-3}$ kg. (b) To reduce the number 1.00795 m to three significant figures, we look at the first three significant figures: 1, 0, and 0. We will definitely use the 1 and the first 0. As for the second 0, we look to the digit to its right, which is a 7, so we will round the 0 up to 1. Therefore, we have 1.01 m if we were to 1.00795 m to three significant figures. (c) To reduce the number 18.9984032 g to five significant figures, we look at the first five significant figures: 1, 8, 9, 9, and 8. We will need to look to the digit to the right of that significant 8, which is 4. This means we need to round this number down. Therefore, we get 18.998 g as the answer. (d) To reduce the number 18.9984032 g to four significant figures, we look at the first four significant figures: 1, 8, 9, and 9. We will need to look to the digit to the right of that significant 8, which is 8. This means we need to round this number up. Therefore, we get 19.00 g as the answer.