Question

1. 0.023
2. 890
3. 91010
4. 1090.0010
5. 0.00120
6. 3.4x10^4

round the following to three significant figures

1. 0.0003045
2. 1020010
3. 780.00
4. 100
5. 918.810
6. 81.20689
7. 6796

calculate the following using the correct number of sig figs.

1. 334.54/198=
2. 34.1/1.1=
3. (2.11x103)/34=
4. 0.0010x0.11=
5. 349x1.10x100=
6. 450/114=
7. 298.01/34.112=
8. 84x31.221=

Explanation:

Step1: Recall significant - figure rules

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

Step2: Round 0.0003045 to 3 significant figures

The first three significant figures are 3, 0, 4. The next digit is 5, so we round up. The result is 0.000305.

Step3: Round 1020010 to 3 significant figures

In scientific notation, \(1020010 = 1.02001\times10^{6}\). Rounding to 3 significant figures gives \(1.02\times 10^{6}\).

Step4: Round 780.00 to 3 significant figures

It is already 780 when rounded to 3 significant figures.

Step5: Round 100 to 3 significant figures

In scientific notation, \(100 = 1.00\times 10^{2}\).

Step6: Round 918.810 to 3 significant figures

The result is 919.

Step7: Round 81.20689 to 3 significant figures

The result is 81.2.

Step8: Round 6796 to 3 significant figures

The result is 6800 (in scientific notation \(6.80\times 10^{3}\)).

Step9: Calculate 334.54/198

\(334.54\div198\approx1.69\) (198 has 3 significant figures, so the result is rounded to 3 significant figures).

Step10: Calculate 34.1/1.1

\(34.1\div1.1\approx31\) (1.1 has 2 significant figures, so the result is rounded to 2 significant figures).

Step11: Calculate \((2.11\times103)/34\)

First, \(2.11\times103 = 2.11\times(100 + 3)=211+6.33 = 217.33\). Then \(217.33\div34\approx6.4\) (34 has 2 significant figures, so the result is rounded to 2 significant figures).

Step12: Calculate \(0.0010\times0.11\)

\(0.0010\times0.11 = 0.00011\) (0.0010 has 2 significant figures, 0.11 has 2 significant figures, so the result has 2 significant figures).

Step13: Calculate \(349\times1.10\times100\)

\(349\times1.10\times100=349\times110 = 38390\approx3.84\times 10^{4}\) (1.10 has 3 significant figures, so the result is rounded to 3 significant figures).

Step14: Calculate 450/114

\(450\div114\approx3.95\) (114 has 3 significant figures, so the result is rounded to 3 significant figures).

Step15: Calculate 298.01/34.112

\(298.01\div34.112\approx8.74\) (34.112 has 5 significant figures, 298.01 has 5 significant figures, and we round to 3 significant figures as per the general rule for division).

Step16: Calculate \(84\times31.221\)

\(84\times31.221 = 2622.564\approx2.6\times 10^{3}\) (84 has 2 significant figures, so the result is rounded to 2 significant figures).

Answer:

1. 0.000305
2. \(1.02\times 10^{6}\)
3. 780
4. \(1.00\times 10^{2}\)
5. 919
6. 81.2
7. \(6.80\times 10^{3}\)
8. 1.69
9. 31
10. 6.4
11. 0.00011
12. \(3.84\times 10^{4}\)
13. 3.95
14. 8.74
15. \(2.6\times 10^{3}\)