How many significant figures are in the measurement, 0.005890 g?

4

6

7

5

8

4 significant figures. Use a rule called the Atlantic-Pacific rule where if the period is absent (Atlantic), you would start counting the numbers from right to left. If the period is present (Pacific), then start counting the numbers from left to right. Since the period is present, start from 5 and there are 4 digits including 5.