Significant Figures!.

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Presentation transcript:

Significant Figures!

There is uncertainty in all measurements. The “certain” digits include all numbers read directly off of the measuring device PLUS one extra estimated digit. Ex: This device is a graduated cylinder. The units are mL. The proper reading should be: 56.0mL (estimated digit)

The amount of definite digits depends on the measuring device. An exact number has no uncertainty, and therefore has an infinite number of sig. figs. Example: There are 25 people in this room, 25.0000000000000000000…. Defined quantities are considered to be exact. Ex: 12 in=1ft, 100cm=1m

Rules for Sig Figs!! All non-zero digits are significant Example: 2.17 - 3 sig. fig. 3894.6 – 5 sig. fig.

2. Leading zeros are never significant Example: 0.003 - 1 sig. fig. 0.04 – 1 sig. fig.

3. Trapped zeros are always significant Example: 205 – 3 sig. fig. 2005 – 4 sig. fig.

4. Trailing zeros are sometimes significant a) They are significant if the number contains a decimal point AND there is a nonzero number before the zero Example: 155.0 – 4 sig. fig. 0.450 – 3 sig. fig.

4. Trailing zeros (cont.) b) They are not sig. if the number does not contain a decimal point even if there are nonzero numbers before it Example: 1550 – 3 sig. fig. 45000 – 2 sig. fig.

(Sig. if there is a decimal) Summary 0.000424000600 Never sig. Always sig. Sometimes sig. (Sig. if there is a decimal)

Practice makes perfect! How many sig figs are in the following? 4.59 3.00 20,020 0.0050 43,000 1.09 x 104 3 3 4 2 2 3

Sig Figs in Calculations Addition and Subtraction: LOOK at the decimal places! The answer is rounded to the same number of decimal places as the number used in the calculation with the least decimal places. Ex: 5.7 11.345 + 2.11 –7.12 7.81~ 4.225 ~ 4.23 7.8

Multiplication and Division: LOOK at the total number of sig figs Multiplication and Division: LOOK at the total number of sig figs! The answer is rounded to the same number of sig. figs. as the number used in the calculation with the least significant figures 0.0561 Ex: 17.85/2.13= x 0.030 8.38028~ 0.001683~ 0.0017 8.38