SIGNIFICANT FIGURES What are Significant Figures The significant

What are Significant Figures? The significant figures in a measurement consist of all the

Your reading might be 76 ml. But, how sure are you that it is

• All measurements are approximations— no measuring device can give perfect measurements without

Measurements are always all measured values plus one approximated value. The pencil is 3.

What is Accuracy? • Accuracy - a measure of how close a measurement is

What is Precision? • Precision – a measure of how close a series of

Rules For Significant Figures 1. Significant figures are used for measured numbers and for

2. Digits from 1 -9 are always significant. Ex. 2342 = 4 significant figures

3. Zeros between two other significant digits are always significant. Ex. 5 055 g

4. One or more additional zeros to the right of both the decimal place

5. Zeros used solely for spacing the decimal point (placeholders) are not significant. Ex.

6. Exact numbers have an infinite number of significant digits but they are generally

Exact equivalences have an unlimited number of significant figures There are exactly 3 feet

SUMMARY EXAMPLES # OF SIG. FIG 453 kg 3 5057 L 4 5. 00

It’s Your Turn To Try! • How many significant figures do the following numbers

1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14)

ASSIGNMENT: Determine the number of significant digits in the following numbers. 1) 5600 _____

Slides: 20

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SIGNIFICANT FIGURES

What are Significant Figures? The significant figures in a measurement consist of all the digits known with certainty plus one final digit, which is uncertain or is estimated.

Your reading might be 76 ml. But, how sure are you that it is really 76 ml? Is it possible that it’s also 75. 99 or 76. 01? CERTAIN VALUE: 75 UNCERTAIN VALUE: 0. 99~1. 1

• All measurements are approximations— no measuring device can give perfect measurements without experimental uncertainty. By convention, a mass measured to 13. 2 g is said to have an absolute uncertainty of plus or minus 0. 1 g and is said to have been measured to the nearest 0. 1 g. In other words, we are somewhat uncertain about that last digit —it could be a "2"; then again, it could be a "1" or a "3". A mass of 13. 20 g indicates an absolute uncertainty of plus or minus 0. 01 g.

Measurements are always all measured values plus one approximated value. The pencil is 3. 6 cm long. 1 2 3 4 5 6 7 With more calibration a more precise measurement is possible The pencil is 3. 64 cm long! 3 4 3. 6 The calibration of the instrument determines measurement precision 3. 7 Now 3. 640 cm !

What is Accuracy? • Accuracy - a measure of how close a measurement is to the true value of the quantity being measured. ►Who is more accurate when measuring a book that has a true length of 17. 0 cm? • Andrea: • 17. 0 cm, 16. 0 cm, 18. 0 cm, 15. 0 cm • Amy: • 15. 5 cm, 15. 0 cm, 15. 2 cm, 15. 3 cm

What is Precision? • Precision – a measure of how close a series of measurements are to one another. A measure of how exact a measurement is. • ►Who is more precise when measuring the same 17. 0 cm book? • Andrea: • 17. 0 cm, 16. 0 cm, 18. 0 cm, 15. 0 cm • Amy: • 15. 5 cm, 15. 0 cm, 15. 2 cm, 15. 3 cm

Rules For Significant Figures 1. Significant figures are used for measured numbers and for numbers derived from measurements; does not include definitions (ex. 1000 ml=1 L) or counting numbers (ex. 1, 2, 3 etc) 10 mm = 1 cm = (2 significant figures) 100 cm = 1 m = (3 significant figures) 1000 g = 1 kg= (4 significant digits)

2. Digits from 1 -9 are always significant. Ex. 2342 = 4 significant figures 25 = 2 significant figures 23. 42 = 4 significant figures

3. Zeros between two other significant digits are always significant. Ex. 5 055 g = 4 significant figures 207 ml = 3 significant figures

4. One or more additional zeros to the right of both the decimal place and another significant digit are significant. • Ex. 5. 00 = 3 significant figures 50. 05 = 4 significant figures 50. 50 = 4 significant figures

5. Zeros used solely for spacing the decimal point (placeholders) are not significant. Ex. 0. 007 (1 significant figure) 1000 ( 1 significant figure) 0. 015 ( 2 significant figures)

6. Exact numbers have an infinite number of significant digits but they are generally not reported. All non zero digits are significant. Ex. 2 ( 1 significant figure) 453 (3 significant figures)

Exact equivalences have an unlimited number of significant figures There are exactly 3 feet in exactly 1 yard. Therefore the 3 can be 3 or 3. 000 etc. and the 1 can be 1 or 1. 000 etc. ! The same is true for:

SUMMARY EXAMPLES # OF SIG. FIG 453 kg 3 5057 L 4 5. 00 g 3 0. 007 ml 1 0. 02300 ml 4 Rules All non-zero digits are always significant. Zeros between 2 sig. dig. are significant. Additional zeros to the right of decimal and a sig. digits are significant. Placeholders are not sig. Zeros to the right of the decimal and to the right of non zeros are significant.

It’s Your Turn To Try! • How many significant figures do the following numbers have?

1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 1234 _____ 0. 023 _____ 890 _____ 91010 _____ 9010. 0 _____ 1090. 0010 _____ 0. 00120 _____ 0. 00030 _____ 1020010 _____ 72 _____ 1000 _____ 918. 010 _____ 0. 0001 _____ 0. 00390 _____ 8120 _____ 1. ) 4 2. ) 2 3. ) 2 4. ) 4 5. ) 5 6. ) 8 7. ) 3 8. ) 2 9. ) 6 10. )2 11. ) 1 12. ) 6 13. ) 1 14. ) 3 15. ) 3

ASSIGNMENT: Determine the number of significant digits in the following numbers. 1) 5600 _____ 2) 45. 00_____ 3) 105. 0_____ 4) 0. 00565_____ 5) 0. 005400_____ 6) 89. 543_____ 7) 5, 056, 300_____ 8) 95. 0540_____ 9) 93, 000_____ 10) 21. 35_____