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Measuring and Units
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International System of UnitsMetric systemSI Universally accepted and understood by
scientist around the world
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Derived units are a combination of base units
Example: m/s
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DensityDensity is a ratio that compares the mass of
an object to its volume. Density = mass/volume D=m/vUnits are
g/L g/mL g/cm3
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Temperature◦C increase 1 unit at a time
Kelvin increase 1 unit at a time
Therefore to convert from ◦C to K K = 273 + ◦C
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Degrees CelsiusBoiling point = 100 ◦CFreezing point = 0 ◦C
SI Unit is KelvinBoiling point = 373 KFreezing point = 273 K
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Scientific NotationContains a number and then raised to a
power
The exponent tell you how many times the factor must be multiplied by ten
If the number is less then 1 the exponent is negative
If the number is greater then 1 the exponent is positive
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When adding or subtracting using exponents, the exponents must be the same
If they are not the same in the problem you can change them so they are the same
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When multiplying and dividing exponents the exponents do not have to be the same.
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When multiplying first multiply the factors then you add the exponents
When dividing first divide the factors then you subtract the exponents
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Dimensional AnalysisDimensional analysis is a method focused on
units that describe matter
Use conversion factors to convert from one unit to another
35 m = 35000 mmConversion factor 1m = 1000mm
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Accuracy and PrecisionAccuracy refers to how close a measured
value is to an accepted value
Precision refers to how close a series of measurements are to each other
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Percent ErrorPercent error is the ratio of error to an
accepted value.
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Percent ErrorA student performs an experiment and determines
the density of an object to be 1.54 g/mL. The actual density is 1.58 g/mL. Find the students percent error.
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Significant FiguresSignificant Figures (sig figs) are the digits
that carry meaning contributing to its precision.
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Rules for Sig Figs1) ALL non-zero numbers (1,2,3,4,5,6,7,8,9)
are ALWAYS significant. 2) ALL zeroes between non-zero numbers are
ALWAYS significant. 3) ALL final zeroes which are to the right of
the decimal point are significant4) Zeros that act as placeholders are not
significantWhen in scientific notation if you can remove
the zeros they are not significant
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ExamplesRule 1 –
456 has 3 significant figures
Rule 2 – 507 has 3 significant figures
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Rule 3 – 9.70 has 3 significant figures
Rule 4 – 0.0787 has only 3 significant figures4350 has only 3 significant figures
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RoundingA calculated number should only have the
number of significant figures as the data with the fewest sig figs.
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Rules for Rounding1. If the digit to the immediate right of the last
significant figures is less than five, do not change the last significant figure
We need only 3 sig figs1. 3.562 3.56
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2. If the digit to the immediate right of the last significant figure is greater than five, round up the last significant figure
3 sig figs
1. 4.567 4.57
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3. If the digit to the immediate right of the last significant figure is equal to five and is followed by a nonzero digit, round up the last significant figure
2.5351 2.54
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4. If the digit to the immediate right of the last significant figure is equal to five and is not followed by a nonzero digit, look at the last significant figure. If it is an odd digit, round it up. If it is an even digit, do not round up.
2.5350 2.54
2.5250 2.52
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Adding and SubtractingWhen you add or subtract measurements,
your answer must have the same number of digits to the right of the decimal point as the value with the fewest digits to the right of the decimal point.
Example:1.24 mL + 12.4 mL = 13.84 mL – 13.8
mL
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Multiplying and DividingWhen multiplying and dividing, your answer must
have the same number of sig figs as the measurement with the fewest sig figs.
3.65 cm x 3.20 x 2.05 cm = 23.944 cm3 = 23.9 cm3