Chem
Unit Conversion
Unit conversions are essential in science for changing measurements from one unit to another.
Example: Converting meters to yards.
Given: 35.0 meters.
Conversion factor: 1 meter = 1.094 yards.
Set up the conversion: Multiply by the conversion factor to find the equivalent in yards.
Important: There can be multiple ways to approach conversion problems.
Significant Figures
Significant figures (sig figs) indicate the precision of a measured number.
Significant figures are crucial in scientific calculations.
Distinction between counted values and measured values:
Counted values (e.g., 12) are exact; they don't have uncertainty.
Measured values have inherent uncertainty.
Rules for Significant Figures
Nonzero digits are always significant.
Example: 536 has 3 significant figures.
Zeros between nonzero digits are significant.
Example: 6,703 has 4 significant figures.
Leading zeros (those to the left of the first nonzero digit) are not significant.
Example: 0.0043 has 2 significant figures.
Trailing zeros to the right of a decimal point are significant.
Example: 45.00 has 4 significant figures.
Example: 7,000 has 1 significant figure without a decimal.
Precision vs. Accuracy
Precision: How close a series of measurements are to each other (agreement among values).
Accuracy: How close a measured value is to the true value.
Possible to be precise but not accurate due to instrument error.
Error in Measurement
Systematic error: Consistent bias in measurements (always higher or lower).
Random error: Unpredictable fluctuations in measurements, requiring multiple data points for accuracy.
Addition and Subtraction Rules
When adding or subtracting, the result should have the same number of decimal places as the measurement with the least decimal places.
Example: 100 + 0.05 would give a result with no decimal places (rounded accordingly).
Multiplication and Division Rules
During multiplication and division, the result should have the same number of significant figures as the measurement with the least significant figures.
Example: If one value has 3 sig figs and another has 1, report the answer with 1 significant figure.
Scientific Notation
Numbers written in scientific notation retain significant figures in their coefficients.
Example: 3.010 × 10^3 has 4 significant figures, while 0.0310 can be expressed as 3.10 × 10^-2 with 3 significant figures.
Measurement Examples
544 kilometers: 3 significant figures (all nonzero).
7 pennies: Infinite significant figures (exact count).
0.06000: 3 significant figures (leading zeros not counted, trailing zeros are significant).
Measurement Instruments
The precision of a measurement depends on the instrument's graduation; estimations are often needed when reading instruments.
Example: Meniscus reading in a graduated cylinder.
Summary
Understand how to perform unit conversions, determine significant figures, and apply rules for precision and accuracy when conducting scientific measurements.
Regular practice and familiarity with these concepts will aid in exam preparation.