Significant digits are crucial in chemistry for accurate measurements and calculations. This resource outlines the rules for identifying significant figures in various numerical contexts. It includes examples and exercises to practice determining significant digits and rounding numbers appropriately. Ideal for chemistry students and educators, this guide enhances understanding of measurement precision and its importance in scientific work.

Key Points

  • Explains the rules for identifying significant digits in measurements.
  • Includes examples of significant figures in various numerical contexts.
  • Provides exercises for practicing significant digit identification and rounding.
  • Highlights the importance of significant figures in scientific accuracy.
newtopiccyclegrowin
3 pages
Language:English
Type:Worksheet
Chemistry
newtopiccyclegrowin
3 pages
Language:English
Type:Worksheet
Chemistry
269
/ 3
Chemistry: Significant Digits
1. Significant numbers are always measurements and thus should always be accompanied by the
measurement's unit. For simplicity, units are not included in the following examples.
2. Any numbers (that are measurements) other than zero are significant. (Many times the zeros are also
significant as you will see below.) Thus 123.45 contains five significant digits.
3. Any zeros between numbers are significant, thus 1002.05 contains six significant digits.
4. Unless told differently, all zeros to the left of an understood decimal point (a decimal that is not printed)
but to the right of the last number are not significant. The number 921000 contains three significant
digits.
5. Any zeros to the left of a number but to the right of a decimal point are not significant.
921000. has six significant digits.
6. These zeros are present merely to indicate the presence of a decimal point (they are used as place
holders), (these zeros are not part of the measurement). The number 0.00123 has three significant
digits. The reason that these zeros are not significant is that the measurement 0.00123 grams is
equal in magnitude to the measurement 1.23 milligrams. 1.23 has three significant digits, thus
0.0123 must also have three significant digits.
7. Any zeros to the right of a number and the right of a decimal point are significant. The value 0.012300
and 25.000 both contain five significant digits. The reason for this is that significant figures indicate to
what place a measurement is made. Thus the measurement 25.0 grams tells us that the
measurement was made to the tenths place. (The accuracy of the scale is to the tenths place.)
Give the number of significant digits in each of the following measurements:
1. 1278.50 __________ 7. 8.002 __________ 13. 43.050 __________
2. 120000 __________ 8. 823.012 __________ 14. 0.147 __________
3. 90027.00 __________ 9. 0.005789 __________ 15. 6271.91 __________
4. 0.0053567 __________ 10. 2.60 __________ 16. 6 __________
5. 670 __________ 11. 542000. __________ 17. 3.47 __________
6. 0.00730 __________ 12. 2653008.0 __________ 18. 387465 __________
Round off the following numbers to three significant digits:
19. 120000 _______________ 22. 4.53619 _______________
20. 5.457 _______________ 23. 43.659 _______________
21. 0.0008769 _______________ 24. 876493 _______________
In an attempt to get away from the mathematical burden of uncertainties, scientists have gone to the use
of established rules for significant digits that have greatly simplified calculations. These rules are:
Chemistry: Significant Digits (continued)
Significant figures in derived quantities (Calculations)
In all calculations, the answer must be governed by the least significant figure employed.
ADDITION AND SUBTRACTION: The answer should be rounded off so as to contain the same number
of decimal places as the number with the least number of decimal places. In other words, an answer can
be only as accurate as the number with the least accuracy.
Thus: 11.31 + 33.264 + 4.1 = 48.674 Rounded off to 48.7
MULTIPLICATION AND DIVISION: The answer should be rounded off to contain the same number of
digits as found in the LEAST accurate of the values.
Thus: 5.282 x 3.42 = 18.06444 Rounded off to 18.1
Perform the following operations giving the proper number of significant figures in the answer:
25. 23.4 x 14 _______________
26. 7.895 + 3.4 _______________
27. 0.0945 x 1.47 _______________
28. 0.005 - 0.0007 _______________
29. 7.895 / 34 _______________
30. 0.2 / 0.0005 _______________
31. 350.0 - 200 _______________
32. 27.68 - 14.369 _______________
33. 3.08 x 5.2 _______________
34. 0.0036 x 0.02 _______________
35. 4.35 x 2.74 x 3.008 _______________
36. 35.7 x 0.78 x 2.3 _______________
37. 3.76 / 1.62 _______________
38. 0.075 / 0.030 _______________
39. 65 000(0.08 x 200 x 0.004) / (800 x 300) _______________
40. [(11.34 −
−−
− 9.63) / 11.34] ×
××
× 100.00 _______________
41. [( 2.0265 −
−−
− 2.02) / 2.0265] ×
××
× 100.00 _______________
Answers to Significant Digit Worksheet:
Give the number of significant digits in each of the following measurements:
1. 1 278.50 6 7. 8.002 4 13. 43.050 5
2. 120 000 2 8. 823.012 6 14. 0.147 3
3. 90 027.00 7 9. 0.005789 4 15. 6271.91 6
4. 0.0053567 5 10. 2.60 3 16. 6 1
5. 670 2 11. 542 000. 6 17. 3.47 3
6. 0.00730 3 12. 2 653 008.0 8 18. 387 465 6
Round off the following numbers to three significant digits:
19. 120 000 = 1.20 x 10
5
22. 4.53619 = 4.54
20. 5.457 = 5.46 23. 43.659 = 43.7
21. 0.0008769 = 0.000877 or 8.77 x 10
-4
24. 876 493 = 876 000 or 8.76 x 10
5
Perform the following operations giving the proper number of significant figures in the answer.
25. 23.4 x 14 327.6 = 330 or 3.3 x 10
2
26. 7.895 + 3.4 11.295 = 11.3
27. 0.0945 x 1.47 0.138 915 = 0.139
28. 0.005 - 0.0007 0.0043 = 0.004
29. 7.895 / 34 0.232 205 882 = 0.23
30. 0.2 / 0.0005 400 = 400
31. 350.0 - 200 150 = 200
32. 27.68 - 14.369 13.311 = 13.31
33. 3.08 x 5.2 16.016 = 16
34. 0.0036 x 0.02 0.000072 = 0.00007
35. 4.35 x 2.74 x 3.008 35.852352 = 35.9
36. 35.7 x 0.78 x 2.3 64.0458 = 64
37. 3.76 / 1.62 2.320987654 = 2.32
38. 0.075 / 0.030 2.5 = 2.5
39. 65 000(0.08 x 200 x 0.004) / (800 x 300) 0.01666666667 = 0.02
40. [(11.34 − 9.63) / 11.34] × 100.00 15.079365079 = 15.1
41. [( 2.0265 − 2.02) / 2.0265] × 100.00 0.3207500617 = 0.5
Converting between two sets of units never changes the number of significant figures in a
measurement. Remember, data are only as good as the original measurement, and no later
manipulations can clean them up.
/ 3
End of Document
269

You May Also Like

FAQs

What are significant digits in measurements?
Significant digits are the digits in a measurement that contribute to its precision. According to the document, any non-zero numbers are always considered significant. Additionally, zeros between non-zero digits are also significant. For example, the number 123.45 contains five significant digits, while 1002.05 contains six significant digits.
How do you determine significant digits in zeros?
The document outlines specific rules for determining the significance of zeros in measurements. Zeros between non-zero digits are always significant, while leading zeros to the left of a decimal point are not significant. For instance, in the measurement 921000, only three digits are significant, but in 921000.0, all six digits are significant.
What is the rule for addition and subtraction regarding significant figures?
In addition and subtraction, the result must be rounded to contain the same number of decimal places as the measurement with the least number of decimal places. For example, if you add 11.31, 33.264, and 4.1, the answer should be rounded to 48.7, reflecting the least precise measurement.
How do you round numbers to significant digits?
The document provides a method for rounding numbers to a specified number of significant digits. For example, to round 120000 to three significant digits, it is expressed as 1.20 x 10^5. Similarly, 4.53619 rounded to three significant digits becomes 4.54.
What is the rule for multiplication and division in significant figures?
When performing multiplication and division, the result should be rounded to contain the same number of significant figures as the measurement with the least significant figures. For instance, if you multiply 5.282 by 3.42, the answer should be rounded to 18.1, as it reflects the least precise measurement.
How many significant digits does the number 0.0053567 have?
According to the document, the number 0.0053567 contains five significant digits. The leading zeros are not counted as significant because they only serve as placeholders, while the digits 5, 3, 5, 6, and 7 are all significant.
What does the presence of trailing zeros indicate in a measurement?
The document states that trailing zeros to the right of a decimal point are considered significant. For example, the number 25.000 contains five significant digits, indicating that the measurement was made to the thousandths place, thus reflecting the precision of the measurement.

Related