CH. 1 - MEASUREMENT

I. Units of Measurement

Scientific Method

A. Derived Units Combination of base units.

Volume (mL or cm3) Formulas for volume of

sphere and cylinder

D = mV

1 cm3 = 1 mL1 dm3 = 1 L

Density (g/mL or g/cm3) mass per volume

B. Density

Density of a substance determines whether that substance will float or sink in a liquid

Density of a substance does not change

LiquidsMaterial Density (gm cm-3)

Water at 4 C 1.0000

Water at 20 C 0.998

Gasoline 0.70

Mercury 13.6

Milk 1.03

SolidsMaterial Density (gm cm-3)

Magnesium 1.7

Aluminum 2.7

Copper 8.3-9.0

Gold 19.3

Iron 7.8

Lead 11.3

Platinum 21.4

Uranium 18.7

Osmium 22.5

Ice at 0 C 0.92

B. DensityM

ass

(g)

Volume (cm3)

Δx

Δyslope D

V

m

B. Density Direct Proportion

Inverse Proportion

y

x

y

x

C. Measurement

Measurement is uncertain because

1. Instruments may have errors

2. Involves estimation

Measurement =

all certain digits + 1 uncertain digit

(estimate)

Accuracy vs. Precision Accuracy - how close a measurement is to the accepted value

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

ACCURATE = CORRECT

PRECISE = CONSISTENT

D. Percent Error

Indicates accuracy of a measurement

100literature

literaturealexperimenterror %

your value(observed value) accepted value

D. Percent ErrorA student determines the density of a

substance to be 1.40 g/mL. Find the % error if the accepted value of the density is 1.36 g/mL.

100g/mL 1.36

g/mL 1.36g/mL 1.40error %

% error = 2.9 %

E. Significant Figures Indicate precision of a measurement.

Recording Sig Figs Sig figs in a measurement include the known digits plus a final estimated

digit

2.32 cm

Sig Fig Rules

1) 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 zeroes which are SIMULTANEOUSLY to the right of the decimal point AND at the end of the number are ALWAYS significant. 4) ALL zeroes which are to the left of a written decimal point and are in a number >= 10 are ALWAYS significant.(Helpful way to check rules 3 and 4 is to write the number in scientific notation. If you can/must get rid of the zeroes, then they are NOT significant.)

Sig Fig Examples

Number # Significant Figures Rule(s)

48,923 5 1

3.967 4 1

900.06 5 1,2,4

0.0004 (= 4 E-4) 1 1,4

8.1000 5 1,3

501.040 6 1,2,3,4

3,000,000 (= 3 E+6) 1 1

10.0 (= 1.00 E+1) 3 1,3,4

E. Significant Figures Counting Sig Figs

Count all numbers EXCEPT: Leading zeros -- 0.0025

what about:60.0025

Trailing zeros without a decimal point -- 2,500

what about: 2500.0

4. 0.080

3. 5,280

2. 402

1. 23.50

E. Significant Figures

Counting Sig Fig Examples

1. 23.50

2. 402

3. 5,280

4. 0.080

4 sig figs

3 sig figs

3 sig figs

2 sig figs

E. Significant Figures Calculating with Sig Figs

Multiply/Divide - The # with the fewest sig figs determines the # of sig figs in the answer.

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

324 g

4 SF 3 SF3 SF

E. Significant Figures Calculating with Sig Figs (con’t)

Add/Subtract - The # with the lowest decimal value determines the place of the last sig fig in the answer.

3.75 mL

+ 4.1 mL

7.85 mL

7.9 mL

3.75 mL

+ 4.1 mL

7.85 mL

20.0685+ 4.25 24.3185 ??

F. Scientific Notation

Converting into Sci. Notation:

Move decimal until there’s 1 digit to its left. Places moved = exponent.

Large # (>1) positive exponentSmall # (<1) negative exponent

Only include sig figs.

65,000 kg 6.5 × 104 kg

F. Scientific Notation

1. 2,400,000 g

2. 0.00256 kg

3. 7 10-5 km

4. 6.2 104

mm

Practice Problems

2.4 106 g

2.56 10-3 kg

0.00007 km

62,000 mm