Ch. 3, Scientific Measurement
Measurement
• Measurement: A quantity that has a number
and a unit. Like 52 meters.
Scientific Notation
• Writing long numbers as smaller ones to a
power of ten.
• 1,400,000 =
1.4 x 106 = 1.4E6
• .00056 = 5.6 x 10 —4
= 5.6E-4
• 15,093,000 = 1.5093 x 107 = 1.5093E7
Accuracy vs. Precision
• *Accuracy: How close
a measurement
comes to the correct
value.
• *Precision: How close
a series of
measurements are to
one another.
Determining Error of a measurement
• Error = Experimental Value - Accepted Value
– Can be positive or negative
• Percent Error = error / accepted value * 100%
– or
– Always positive
• Example, you measured 99 cm, but it is 100 cm.
• Significant Figures: The digits in a
measurement that are known plus one
that is not known.
– Filled 43.1 mL
Rules for Sig Figs
• Non-Zero Numbers are always significant
– Ex) .236 m has 3 sig figs.
• Zeros between non-zero numbers are significant.
– Ex) 7003 m and 40.79 m each have 4 sig figs.
• Leftmost zeros are not significant
– Ex) .000099 m, 0.42 m, and .073 m each have 2 sig figs.
• Rightmost zeros are significant if they come before or after
a period.
– Ex) 9000. m, 90.00 m, and 9.090 m each have 4 sig figs.
Rules for Sig Figs
• Rightmost zeros with no decimal points are no
significant.
• Ex) 300 m has 1 sig fig.
• Exactly defined quantities have an unlimited number
of sig figs.
• Seen most when converting between
measurements.
• 60 min = 1 hour, 100 cm = 1 m each have an
unlimited number of sig figs.
Is a Zero a Significant Number or Not?
•
•
•
•
504 L
.06 mL
50.0 m
7,000 km
Sig Figs in Calculations:
• Calculations cannot be more precise than the least precise
measurement.
• Addition or subtraction - Round the final answer to the
same number of decimal places as the measurement with
the least number of decimal places.
– the last “shared column”.
• 13.4 m + 5.254 m = 18.7 m
Sig Figs in Calculations:
• Multiplication or Division - The final answer
should have the same number of sig figs as
the measurement that has the least number
of sig figs.
• 2.4526 m x 8.4 m = 21 m
• In this class, delay rounding until the very end.
• (3.449L + 6.57L) * 8.779L / 5.2L = 17L
International System of Units
• How much of
something you have is
given by Units. Like
centimeters, kilometers,
etc.
• SI is the standard
measurement system
for science.
•
•
•
•
•
•
•
* The five SI units used most by chemists are:
Distance = meter (m)
Mass = kilogram (kg)
Temperature = kelvin (K)
Time = second (s)
Volume = liter (L)
Amount = mole (mol).
• Prefixes can be used in front of units for
powers of 10.
• Mass = how much “stuff” is in
something. How much
matter is in something.
• Weight = the pull on
something by gravity.
• If I go to the moon, which
changes and which stays
constant?
-Weight changes, mass stays the same.
Temperature:
• Celsius and Kelvin are units of temperature
that are the same, just shifted.
• K = C + 273
• Water freezes at 0 C and at 273 K.
• Absolute Zero = 0 K;
a K value will never be
negative.
*Energy
• * Energy - The ability to do work or produce
heat.
• Joule (J) is the SI unit of energy.
• Calorie (cal) is another unit of energy.
• 1 J = .239 cal
Conversions
Convert 7 mm to m.
Convert 12.4 Mm to cm.
• Convert 7 km/ms to m/s
• An experiment asks students to measure 1.50 g
of Cu wire. All we have is a 40.0 g spool of Cu.
How many students can do the experiment?
*Density
• *Density = mass / volume
• What is the density of 2 g of salt in a volume
of 4 L?
• What is the density in g/L of 5 kg of salt in a
volume of 6 mL?
If silver has a density of 10.5 g/L, what is
the volume of a silver coin that has a
mass of 14 g?
• Density decreases as temperature increases.
• D=m/v
• As T increases, V increases.
• Therefore, density decreases.
Example Problems!!!
• 1. How many sig figs in: 1.480*105
.00070
1.000080
3.00E3
• 2. Perform these calculations and come up with answers
that have the correct number of sig figs:
5.667 + .34
5.007E3 / 1.20
4.3 - 1.3590
5.309E3 * 3
• 3. Convert 3.4 ng into kg.
• 4. Convert 7E3 cm into Mm.
• 5. What is the mass if a substance with a density of
4.5 g/L has a volume of 3 L?
6. How many sig figs in:
1010
3000
3000.
3000.0
7. Convert 3 kg into g.
Convert 34 cm into m.
Convert 4 m into cm.
8. You have a 4 kg box. You measure it to be 5.8 kg. What
is the error? The % error?
9. What is the difference between mass and weight?
Accuracy and precision?
• 11. Put 5,009,000,000 into Scientific Notation
• 12. Put 0.00007890 into Scientific Notation.
• 13. Put 8.7 * 10-4 into a regular number.
• 14. Which is the largest amount?
• A. 2*102 g
B. 30 kg
C. 45 mg D. 190 g
• 15. Convert 40 Kelvin into Celsius
• 16. Convert 99 Celsius into Kelvin.