Ch. 3, Scientific Measurement

Measurement

• : A quantity that has a and a . Like 52 meters.

Scientific Notation

• Writing long numbers as smaller ones to a power of ten.

• = 1.4 x 106 = 1.4E6• .00056 = = 5.6E-4• 15,093,000 = 1.5093 x 107 =

Accuracy vs. Precision• * : How

close a measurement comes to the value.

• * : How close a series of measurements are to .

Determining Error of a measurement

• = Experimental Value - Accepted Value– Can be positive or

• Percent Error = error / accepted value * 100%– or

– Always • Example, you measured 99 cm, but it is 100 cm.

• : 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 sig figs.• Zeros between non-zero numbers are significant.

– Ex) 7003 m and 40.79 m each have sig figs.• Leftmost zeros are not significant

– Ex) .000099 m, 0.42 m, and .073 m each have 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 sig figs.

Rules for Sig Figs• Rightmost zeros with no decimal points are no

significant.• Ex) 300 m has sig fig.

• Exactly defined quantities have an 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 be more precise than the precise measurement.

• Addition or subtraction - Round the final answer to the same number of decimal places as the measurement with the 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 number of sig figs as the measurement that has the 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.

• is the standard measurement system for science.

International System of Units

• * The five SI units used most by chemists are: • Distance = (m) • Mass = kilogram (kg)• Temperature = (K)• Time = second (s)• Volume = liter (L)• Amount = (mol).

• Prefixes can be used in front of units for powers of 10.

• = how much “stuff” is in something. How much matter is in something.

• = the pull on something by gravity.

• If I go to the moon, which changes and which stays constant?

- changes, stays the same.

Temperature:

• Celsius and Kelvin are units of temperature that are the , just shifted.

• K = C + 273• Water freezes at 0 C and at K.• Absolute Zero = 0 K; a K value will never be

negative.

*Energy

• * - The ability to do work or produce heat.

• (J) is the SI unit of energy.

• (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

• * = 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 as temperature increases.

• D=m/v• As T increases, V .• 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.

More from Chp 3

• I. Using Measurements

A. Accuracy vs. Precision

• - how close a measurement is to the accepted value

• - how close a series of measurements are to each other

ACCURATE = CORRECT

PRECISE = CONSISTENT

C. Significant Figures

• Indicate precision of a measurement.

• Recording Sig Figs– Sig figs in a measurement include the _

digits plus a final digit– (See page 24)

2.32 cm

• 1) How many sig figsafter we estimate?

• 2) Now how many?

C. Significant Figures

• Counting Sig Figs

– Count all numbers EXCEPT:

• _______________zeros -- 0.0025

• Trailing zeros _________________a decimal point -- 2,500

4. 0.080

3. 5,280

2. 402

1. 23.50

C. Significant Figures

Counting Sig Fig Examples

1. 23.50

2. 402

3. 5,280

4. 0.080

sig figs

sig figs

sig figs

sig figs

C. Significant Figures

• Calculating with Sig Figs– Multiply/Divide - The # with the

sig figs determines the # of sig figs in the answer.

(13.91g/cm3)(23.3cm3) = 324.103g

C. Significant Figures

• Calculating with Sig Figs (con’t)– Add/Subtract - The # with the

decimal value determines the place of the last sig fig in the answer.

3.75 mL

+ 4.1 mL

7.85 mL

3.75 mL

+ 4.1 mL

7.85 mL

C. Significant Figures

• Calculating with Sig Figs (con’t)– Exact Numbers do not limit the # of sig figs in

the answer.• Counting numbers: 12 students• Exact conversions: 1 m = 100 cm• “1” in any conversion: 1 in = 2.54 cm

C. Significant Figures

5. (15.30 g) ÷ (6.4 mL)

Practice Problems

= 2.390625 g/mL

6. 18.9 g

- 0.84 g

18.06 g

D. Scientific Notation

• Converting into Sci. Notation:– Move decimal until there’s digit to its left.

Places moved = .

– Large # (>1) exponentSmall # (<1) exponent

– Only include sig figs.

65,000 kg 6.5 × 104 kg

D. Scientific Notation

7. 2,400,000 g

8. 0.00256 kg

9. 7 10-5

km

10. 6.2 104

mm

Practice Problems

D. Scientific Notation

• Calculating with Sci. Notation (5.44 x 107 g) / (8.1 x 104 mol) =

Type of your calculator:

5.44 EE 7 / 8.1 EE 4 =

671.6049383

E. SI Units

Quantity Base Unit Abbrev.

Length

Mass

Time

Temp

meter

kilogram

second

kelvin

s

K

Amount mole

Symbol

l

m

t

n

E. SI Units

mega- M 106

deci- d 10-1

centi- c 10-2

milli- m 10-3

Prefix Symbol Factor

micro- 10-6

nano- n 10-9

pico- p 10-12

kilo- k 103

BASE UNIT --- 100

F. Derived Units

• Combination of base units.

• (m3 or cm3) – length length length

D = MV

1 cm3 = 1 mL1 dm3 = 1 L

(kg/m3 or g/cm3)mass per volume

Problem-Solving Steps

1. _

2. Plan

3. Compute

4. _

Density

• An object has a volume of 825 cm3 and a density of 13.6 g/cm3. Find its mass.

GIVEN:

V = D =

M = ?

WORK:

M = M =

M =

V

MD

Density

• A liquid has a density of 0.87 g/mL. What volume is occupied by 25 g of the liquid?

GIVEN:

D =

V = ?

M =

WORK:

V =

V =

V =V

MD

SI Prefix Conversions

mega- M 106

deci- d 10-1

centi- c 10-2

milli- m 10-3

Prefix Symbol Factor

micro- 10-6

nano- n 10-9

pico- p 10-12

kilo- k 103

mo

ve le

ft

mo

ve r

igh

t BASE UNIT --- 100

SI Unit Conversions

• King __doofus can milk many newts.

• k__ d c m m n

• kilo, deci, , milli, ,

• What’s yours?

=

SI Prefix Conversions

NUMBERUNIT

NUMBER

UNIT

532 m = _______ km

SI Prefix Conversions

1) 20 cm = ______________ m

2) 0.032 L = ______________ mL

3) 45 m = ____ mm

4) 805 dm = ______________ km

Dimensional Analysis

• Steps:

1. Identify starting & units.

2. Line up conversion factors so units .

3. Multiply all numbers & divide by each bottom number.

4. Check units & answer.

Dimensional Analysis

• Lining up conversion factors:

1 in = 2.54 cm

2.54 cm 2.54 cm

1 in = 2.54 cm

1 in 1 in

= 1

1 =

Dimensional Analysis

• How many milliliters are in 1.00 quart of milk? (1L = 1.057 qt)

1.00 qt

qt mL

Dimensional Analysis

• You have 1.5 pounds of gold. Find its volume in cm3 if the density of gold is 19.3 g/cm3. (1 kg = 2.2 lbs)

lb cm3

1.5 lb

Dimensional Analysis

5) Your European hairdresser wants to cut your hair 8.0 cm shorter. How many inches will he be cutting off? (1 in=2.54cm)

8.0 cm

cm in