To solve this question, let us remember the basic rules of what counts as a significant figure or digit:

Rule One: All non-zero digits are significant.

Rule Two: All zeroes between significant digits are significant.

Rule Three: All zeroes which are both to the right of the decimal point

and...

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To solve this question, let us remember the basic rules of what counts as a significant figure or digit:

Rule One: All non-zero digits are significant.

Rule Two: All zeroes between significant digits are significant.

Rule Three: All zeroes which are both to the right of the decimal point

andto the right of all non-zero significant digits are significant.

Now, let's solve each part individually:

1) 405000: The number of significant digits is **3**, and the digits are 4, 0, and 5. Using Rule One, the digits 4 and 5 are significant. Using Rule Two, the zero between 4 and 5 is significant. Similarly, using Rule Three, the last three zeroes are non-significant.

2) 0.0098: The number of significant digits is **2** (only 9 and 8 are significant; the zeroes to the right of the decimal point are **not** to the right of non-zero significant digits). The significant digits are 9 and 8.

3) 39.999999: The number of significant digits is **8**. (Hint: all the non-zero digits are significant). The significant digits are 3, 9, 9, 9, 9, 9, 9, and 9.

4) 13.00: The number of significant digits is **4** (the zeroes to the right of the decimal point are significant). The significant digits are 1, 3, 0, and 0.

5) 80,000,089: The number of significant digits is **8 **(hint: Rule Two: zeroes between significant digits are always significant). The significant digits are 8, 0, 0, 0, 0, 0, 8, and 9.

6) 55,430.00: The number of significant digits is **7 **(hint: Rule One and Rule Three). The significant digits are 5, 5, 4, 3, 0, 0, and 0.

7) 0.000033: The number of significant digits is **2 **(hint: Rule One and Rule Three). The significant digits are 3 and 3.

8) 620.03080: The number of significant digits is **8**. The significant digits are 6, 2, 0, 0, 3, 0, 8, and 0.

Hope this helps.