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 to 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.
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