Question

if the decimal is present: find the first nonzero on the left, then count all digits to the right. if the decimal is absent: find the first nonzero on the right, then count all digits to the left. how many significant figures do the following numbers have? 1) 1234 2) 0.023 3) 890 4) 91010 5) 9010.0 6) 1090.0010 7) 0.00120 8) 3.4×10¹ 9) 9.0×10³ 10) 9.010×10¹ 11) 0.00030 12) 1020010 round the following to three significant figures 13) 0.0003045 14) 1020010 15) 780.00 16) 100 17) 918.810 18) 81.20689 19) 6796 calculate the following using the correct number of sig figs. 20) 334.54/198 = 21) 34.1/1.1 = 22) (2.11×103)/34 = 23) 0.0010×0.11 = 24) 349×1.10×100 = 25) 450/114 = 26) 298.01/34.112 = 27) 84×31.221 =

Explanation:

Step1: Determine significant - figures rules

Non - zero digits are always significant. Zeros between non - zero digits are significant. Trailing zeros in a number with a decimal point are significant. Trailing zeros in a number without a decimal point may or may not be significant.

Step2: Count significant figures for each number

1. 1234: All non - zero digits, so 4 significant figures.
2. 0.023: Leading zeros are not significant, 2 significant figures.
3. 890: Trailing zero without decimal, 2 significant figures (assuming no other context).
4. 91010: Trailing zero without decimal, 4 significant figures (assuming no other context).
5. 9010.0: Zeros between non - zero digits and trailing zero with decimal are significant, 5 significant figures.
6. 1090.0010: All digits are significant, 8 significant figures.
7. 0.00120: Leading zeros are not significant, 3 significant figures.
8. 3.4×10¹: 2 significant figures.
9. 9.0×10³: 2 significant figures.
10. 9.010×10⁷: 4 significant figures.
11. 0.00030: Leading zeros are not significant, 2 significant figures.
12. 1020010: Trailing zero without decimal, 6 significant figures (assuming no other context).

Step3: Rounding rules

To round to three significant figures, identify the first three significant figures and round the third one based on the fourth.

1. 0.0003045 rounds to 0.000305.
2. 1020010 rounds to 1.02×10⁶.
3. 780.00 rounds to 780.
4. 100 rounds to 1.00×10².
5. 918.810 rounds to 919.
6. 81.20689 rounds to 81.2.
7. 6796 rounds to 6800 (or 6.80×10³).

Step4: Calculation rules for significant figures

For multiplication and division, the result has the same number of significant figures as the number with the fewest significant figures in the values being multiplied or divided.

1. 334.54÷198 = 1.69 (198 has 3 significant figures).
2. 34.1÷1.1 = 31 (1.1 has 2 significant figures).
3. (2.11×103)÷34=(2.11×103)÷34 = 6.4 (34 has 2 significant figures).
4. 0.0010×0.11 = 1.1×10⁻⁴ (0.0010 has 2 significant figures).
5. 349×1.10×100 = 3.84×10⁴ (1.10 has 3 significant figures).
6. 450÷114 = 3.95 (114 has 3 significant figures).
7. 298.01÷34.112 = 8.74 (34.112 has 5 significant figures, 298.01 has 5 significant figures, result to 3 significant figures as per rules).
8. 84×31.221 = 2.6×10³ (84 has 2 significant figures).

Answer:

1. 4
2. 2
3. 2
4. 4
5. 5
6. 8
7. 3
8. 2
9. 2
10. 4
11. 2
12. 6
13. 0.000305
14. 1.02×10⁶
15. 780
16. 1.00×10²
17. 919
18. 81.2
19. 6800 (or 6.80×10³)
20. 1.69
21. 31
22. 6.4
23. 1.1×10⁻⁴
24. 3.84×10⁴
25. 3.95
26. 8.74
27. 2.6×10³