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

• How much of something you have is given by Units. Like centimeters, kilometers, etc.

• SI is the standard measurement system for science.

International System of Units

• * 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

ConversionsConvert 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.