SIGNIFICANT FIGURES OR DIGITS - Oak Park Independent

[Pages:15]Significant Digits/Figures

Sept. 2, 2014

SIGNIFICANT FIGURES OR DIGITS

? THE NUMBER OF SIGNIFICANT FIGURES INCLUDED IN A CALCULATION OR MEASUREMENT IS DEPENDENT ON THE ACCURACY OF THE MEASURING DEVICE OR INSTRUMENT USED TO MAKE THE ORIGINAL MEASUREMENTS

Exact v. Inexact Numbers

? Exact numbers ? those numbers known exactly (by definition or by counting)

? One dozen = 12, one inch = 2.54 cm, 33 students in the room

? Inexact numbers ? values with some uncertainty; anything measured using a piece of equipment (balance, graduated cylinder)

? Mass of penny = 3.03 grams

Precision v. Accuracy

? Precision ? a measure of how closely individual measurements agree with one another (repeatability)

? A balance is precise if it gives you the same value for every trial

? Accuracy ? how closely individual measurements agree with the correct or "true" value (bullseye)

? a balance is considered more accurate with increasing decimal places (+/- 0.0001 g is more accurate than +/- 0.01 g)

? Greater accuracy of an instrument means more significant figures.

SIGNIFICANT FIGURES

? RULE 1: Digits other than zero are always significant.

Examples: 96g

61.4g 0.52g

2 significant digits 3 significant digits 2 significant digits

SIGNIFICANT FIGURES

? RULE 2: One or more final zeros used after the decimal point are always significant (determined by the accuracy of the measuring device: i.e. - balance or electronic balance, etc.)

Example: 4.72 km

4.7200 km 82.0 m

3 significant digits 5 significant digits 3 significant digits

SIGNIFICANT FIGURES

? RULE 3: Zeros between two other significant digits are always significant.

Example: 5.029 m 306 km 6.02 x 10?? particles

4 significant digits 3 significant digits 3 significant digits

SIGNIFICANT FIGURES

? RULE 4: Zeros used solely for spacing the decimal point are not significant. The zeros are place holders only.

? You can tell a number is a placeholder if when you remove the zeros, the number CHANGES its value

Example:

7000 g

1 significant digit

0.00783 kg

3 significant digits

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