The significant figures in a measurementConsist of all the digits known with certainty plus one final digit, which is uncertain or is estimated.

What are Significant Figures?

CERTAIN VALUE: 75UNCERTAIN VALUE: 0.99~1.1

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?

•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.

1 2 3 4 5 6 7

Measurements are always all measured values plus one approximated value. The pencil is 3.6 cm long.

3 4

With more calibration a more precise measurement is possible The pencil is 3.64 cm long!

3.6 3.7

Now 3.640 cm !The calibration of the instrumentdetermines measurement precision

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 17.0cm?

• Andrea:• 17.0cm, 16.0cm, 18.0cm, 15.0cm• Amy: • 15.5cm, 15.0cm, 15.2cm, 15.3cm

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 17.0cm book?

• Andrea:• 17.0cm, 16.0cm, 18.0cm, 15.0cm• Amy: • 15.5cm, 15.0cm, 15.2cm, 15.3cm

Rules For Significant Figures

1. Significant figures are used for measured numbers and for numbers derived from measurements; does not include

definitions (ex. 1000ml=1L) or counting numbers (ex. 1,2,3 etc)

10 mm = 1cm = (2 significant figures)100cm = 1m = (3 significant figures)1000g = 1kg= (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 3.0 or 3.00 or 3.000 etc. and the 1can be 1 or 1.0 or 1.00 or 1.000 etc. !

The same is true for:

SUMMARYEXAMPLES # OF SIG.

FIGRules

453 kg 3All non-zero digits are always significant.

5057 L 4Zeros between 2 sig. dig. are significant.

5.00 g 3Additional zeros to the right of decimal and a sig. digits are significant.

0.007 ml 1 Placeholders are not sig.

0.02300 ml 4Zeros 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) 1234 _____2) 0.023 _____3) 890 _____4) 91010 _____5) 9010.0 _____6) 1090.0010 _____7) 0.00120 _____8) 0.00030 _____9) 1020010 _____10) 72 _____11) 1000 _____12) 918.010 _____13) 0.0001 _____14) 0.00390 _____15) 8120 _____

1.) 42.) 23.) 24.) 45.) 56.) 87.) 38.) 29.) 610.)211.) 112.) 613.) 114.) 315.) 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, 000_____10) 21.35_____