Question

sig fig worksheet
name
how many significant figures are in each of the following numbers?
(a) 5.432 g
(b) 40.319 g
(c) 146 cm
(d) 3.285 cm
(e) 0.189 s
(f) 429.3 mm
(g) 2873.0 a
(h) 99.9 ml
(i) 0.0000246 g
(j) 144 mol
(k) 2500 cm
(l) 2500.0 cm
(m) 0.0000242 mg
(n) 1.00001 s
(o) 0.00001 s

1. 5.40
2. 210
3. 801.5
4. 1,000
5. 101.0100
6. 1.2×10³
7. 0.00120
8. 0.0102
9. 9.010×10⁴
10. 2,370.0

round these numbers to 3 significant digits.

1. 1,566,311
2. 2.7651×10⁻³
3. 84,592
4. 0.0011672
5. 0.07799

Explanation:

Step1: Recall significant - figure rules

Non - zero digits are always significant. Zeros between non - zero digits are significant. Leading zeros (zeros before non - zero digits) are not significant. Trailing zeros in a number with a decimal point are significant.

Step2: Analyze each number

(a) 5.432 g: All non - zero digits, so 4 significant figures.
(b) 40.319 g: Non - zero digits and zero between non - zero digits, 5 significant figures.
(c) 146 cm: 3 non - zero digits, 3 significant figures.
(d) 3.285 cm: 4 non - zero digits, 4 significant figures.
(e) 0.189 s: Leading zero is not significant, 3 significant figures.
(f) 429.3 mm: 4 non - zero digits, 4 significant figures.
(g) 2873.0 A: Trailing zero with decimal point, 5 significant figures.
(h) 99.9 ml: 3 non - zero digits, 3 significant figures.
(i) 0.0000246 g: Leading zeros are not significant, 3 significant figures.
(j) 144 mol: 3 non - zero digits, 3 significant figures.
(k) 2500 cm: Without decimal point, 2 significant figures.
(l) 2500.0 cm: Trailing zeros with decimal point, 5 significant figures.
(m) 0.0000242 mg: Leading zeros are not significant, 3 significant figures.
(n) 1.00001 s: 6 significant figures (non - zero digits and zeros between non - zero digits).
(o) 0.00001 s: Leading zeros are not significant, 1 significant figure.

1. 5.40: Trailing zero with decimal point, 3 significant figures.
2. 210: Without decimal point, 2 significant figures.
3. 801.5: 4 significant figures (non - zero digits and zero between non - zero digits).
4. 1,000: Without decimal point, 1 significant figure.
5. 101.0100: 7 significant figures (non - zero digits and zeros between non - zero digits and trailing zeros with decimal point).
6. \(1.2\times10^{3}\): 2 significant figures (\(1\) and \(2\)).
7. 0.00120: Leading zeros are not significant, 3 significant figures.
8. 0.0102: Leading zeros are not significant, 3 significant figures.
9. \(9.010\times 10^{4}\): 4 significant figures (\(9\), \(0\), \(1\), \(0\)).
10. 2370.0: 5 significant figures (non - zero digits and trailing zero with decimal point).

Step3: Round numbers to 3 significant digits

1. 1,566,311: \(1.57\times 10^{6}\) (rounding 1566311 to 1570000 and writing in scientific notation).
2. \(2.7651\times 10^{-3}\): \(2.77\times 10^{-3}\) (rounding 2.7651 to 2.77).
3. 84,592: \(84.6\times 10^{3}\) or 84600 (rounding 84592 to 84600).
4. 0.0011672: 0.00117 (rounding 0.0011672 to 0.00117).
5. 0.07799: 0.0780 (rounding 0.07799 to 0.0780).

Answer:

(a) 4
(b) 5
(c) 3
(d) 4
(e) 3
(f) 4
(g) 5
(h) 3
(i) 3
(j) 3
(k) 2
(l) 5
(m) 3
(n) 6
(o) 1

1. 3
2. 2
3. 4
4. 1
5. 7
6. 2
7. 3
8. 3
9. 4
10. 5
11. \(1.57\times 10^{6}\)
12. \(2.77\times 10^{-3}\)
13. 84600
14. 0.00117
15. 0.0780