Question

physics: significant digits
give the number of significant digits in each of the following measurements:

1. 1278.50
2. 120000
3. 90027.00
4. 0.0053567
5. 670
6. 0.00730
7. 8.002
8. 823.012
9. 0.005789
10. 2.60
11. 542000.
12. 2653008.0
13. 43.050
14. 0.147
15. 6271.91
16. 6
17. 3.47
18. 387465

round off the following numbers to three significant digits:

1. 120000
2. 5.457
3. 0.0008769
4. 4.53619
5. 43.659
6. 876493

perform the following operations giving the proper number of significant figures in the answer:

1. 23.4 × 14
2. 7.895 + 3.4
3. 0.0945 × 1.47
4. 0.005 - 0.0007
5. 7.895 / 34
6. 0.2 / 0.0005

significant digit rules
significant figures are critical when reporting scientific data because they give the reader an idea of how well you could actually measure/report your data. before looking at a few examples, lets summarize the rules for significant figures.

1. all non - zero numbers (1,2,3,4,5,6,7,8,9) are always significant.
2. all zeroes between non - zero numbers are always significant.
3. all trailing zeros are significant. ex. 1.65000 has 6 sig. figs
4. all leading zeros are not significant. ex. 0.0065 has only two sig. figs.

Explanation:

Step1: Determine significant digits for 0.0008769

Leading zeros are not significant. Non - zero digits \(8,7,6,9\) are significant.

Step2: Round 0.0008769 to three significant digits

The first three non - zero digits are \(8,7,6\). The next digit is \(9\gt5\), so we round up the third digit. \(0.0008769\approx0.000877\) (in scientific notation \(8.77\times10^{-4}\))

Step3: Round 876493 to three significant digits

The first three digits are \(8,7,6\). The next digit is \(4\lt5\), so we keep the third digit as it is. \(876493\approx876000\) (in scientific notation \(8.76\times 10^{5}\))

Step4: Calculate \(23.4\times14\)

\(23.4\times14 = 327.6\). For multiplication, the number of significant digits is determined by the number with the least significant digits. \(23.4\) has three significant digits and \(14\) has two. We round to two significant digits: \(330\)

Step5: Calculate \(7.895 + 3.4\)

\(7.895+3.4=11.295\). For addition, we consider the decimal places. \(3.4\) has one decimal place. We round to one decimal place: \(11.3\)

Step6: Calculate \(0.0945\times1.47\)

\(0.0945\times1.47 = 0.138915\). \(0.0945\) has three significant digits and \(1.47\) has three. We round to three significant digits: \(0.139\)

Step7: Calculate \(0.005 - 0.0007\)

\(0.005-0.0007 = 0.0043\). For subtraction, we consider the decimal places. \(0.005\) has three decimal places and \(0.0007\) has four. We round to three decimal places: \(0.004\)

Step8: Calculate \(7.895\div34\)

\(7.895\div34\approx0.2322\). \(7.895\) has four significant digits and \(34\) has two. We round to two significant digits: \(0.23\)

Step9: Calculate \(0.2\div0.0005\)

\(0.2\div0.0005 = 400\). \(0.2\) has one significant digit and \(0.0005\) has one. We round to one significant digit: \(400\)

Answer:

1. \(0.000877\) (or \(8.77\times 10^{-4}\))
2. \(876000\) (or \(8.76\times 10^{5}\))
3. \(330\)
4. \(11.3\)
5. \(0.139\)
6. \(0.004\)
7. \(0.23\)
8. \(400\)