MEASUREMENTS

What is the difference between these two measurement rulers?Should we record the same number for each scale reading?

The second scale gives us more information, it is more precise.

To indicate how precise our measurement tool is, we use significant figures.Significant figures – These are all the digits you know for sure + one place that is an estimate.

It is also important to indicate how uncertain we are in our measurements.Uncertainty - Limit of precision of the reading (based on your ability to estimate the final digit).

How many time could you imagine dividing the smallest increment?

How many time could you imagine dividing the smallest increment?

How many time could you imagine dividing the smallest increment?

Significant Digits or Significant Figures

• We must be aware of the accuracy limits of each piece of lab equipment that we use and record our data to the proper number of significant figures.

• You are always allowed one estimated figure in measurements

• When measured quantities are given to you, it is assumed that the proper number of significant figures were recorded.

Rules for Counting Significant Figures

• All non-zero digits are significant.1 473 _____ 785 _____ 387.56 ____

• Zeros:– Leading Zeros are not significant.

0.421 _____ 0.5 _____ 0.0011 _____– Captive Zeros are significant.

70 304 _____ 395.01 _____ 1.008 _____– Trailing Zeros are significant if there is a decimal point.

12.380 _____ 1.30 _____ 1691.100 _____– Trailing Zeros are not significant if there is no decimal point.

2 500 _____ 800 _____ 9 010 _____

7

3 5

3 1 2

5 5 4

5 3

4

2 1 3

Determine the amount of significant figures in the following examples:

967 _____0.111 0 _____0.005 670 _____4.530 _____2.700 _____0.006 007 _____9.67 _____0.000 008 _____0.800 008 _____

34

444

43

16

Calculating with Significant Figures

• Multiply/Divide: The number with the fewest number of sig figs will determine the number of sig figs in the answer.– Example

(13.92 g/cm3)(23.3 cm3 ) = 324.103 g4 sig figs 3 sig figs 3 sig figs

324 g

Calculating with Significant Figures

• Addition/Subtraction: The number with the fewest amount of decimal places determines the amount of decimal places in the answer .– Example

3.76 g + 14.83 g + 2.1 g = 20.69 g2 decimal

places

20.7 g

2 decimal places

1 decimal places

1 decimal places