Do Now

Take a copy of the worksheet Organizing Data from the front desk.

Bring it back to your seat and work on it for the first 10 min. of class.

Accuracy vs. Precision

Accuracy -- the extent to which a reportedmeasurement approaches the true value of the quantity measured.

the degree of exactness of ameasurement.

Precision--

Accuracy and Precision

Scientific Notation

When numbers are very large or very small it can be very cumbersome to write all those zeros.

For example the mass of the earth is about

5,970,000,000,000,000,000,000,000 kg

scientists prefer to write it this way5.97 x 1024 kg

Scientific NotationScientific notation works by dividing out

the appropriate factor of 10.104 =10,000103 =1,000102 =100101 =10100 =1

10-1 =0.110-2 =0.01

10-3 =0.00110-4 =0.0001

Scientific Notation

7,359,845. m = 7.359845 x 106 m45.6 kg = 4.56 x 101 kg

0.002389 s = 2.389 x 10-3 s

Significant Figures

Significant figures are the digits in a measurement that are known with certainty.

How precise of a measurement can we make with a ruler like this one?

Significant Figures

Significant figures are the digits in a measurement that are known with certainty.

How precisely can we measure mass with a triple beam balance like this one?

Significant Figures

Significant figures are the digits in a measurement that are known with certainty.

Which instrument will give me a more precise volume measurement?

Measure your lab bench.

Go to a bench with your lab group. Have each member measure the length of

the bench with a meter stick and with a video cassette.

Record all the data in a table.

Significant Figure Rules

1.All nonzero digits are significant:

1.243 g has 4 significant figures,

1.2 g has 2 significant figures.

Significant Figure Rules

1.All nonzero digits are significant:

2.Zeros between nonzero digits are significant:

Significant Figure Rules

1.All nonzero digits are significant:

2.Zeros between nonzero digits are significant:

1002 kg has 4 significant figures,

3.07 mL has 3 significant figures.

Significant Figure Rules

1.All nonzero digits are significant:

2.Zeros between nonzero digits are significant:

3.Leading zeros to the left of the first nonzero digits are not significant; such zeroes merely indicate the position of the decimal point:

0.001 mL has only 1 significant figure,

0.012 g has 2 significant figures.

Significant Figure Rules

1.All nonzero digits are significant:

2.Zeros between nonzero digits are significant:

3.Leading zeros to the left of the first nonzero digits are not significant; such zeroes merely indicate the position of the decimal point:

4.Trailing zeros that are also to the right of a decimal point in a number are significant:

5.When a number ends in zeros that are not to the right of a decimal point, the zeroes are not necessarily significant:

190 miles may be 2 or 3 significant figures,

50,600 calories may be 3, 4, or 5 significant figures

Significant Figure Rules

The potential ambiguity in the last rule can be avoided by the use of scientific notation. For example, depending on whether the number of significant figures is 3, 4, or 5, we would write 50,600 calories as:

5.06 x 104 calories (3 significant figures),

5.060 x 104 calories (4 significant figures), or

5.0600 x 104 calories (5 significant figures).

Significant Figures When multiplying

measurements, the answer is only as precise as the LEAST precise measurement.

8.753469 cm

3 cm

Area = length × width = 8.753469 × 3 = 26.260407However our least precise numberis 3 which has one significant figureThereforeArea = 30cm2

Wrap Up

Homework:Complete the worksheet Study Guide: Section 1.3 and bring it in for next class.