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• Homework Policy

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Measuring

Measuring

Measuring

MKS system

MKS – Meter-Kilogram-Second

Meter• Originally 1/10,000,000 the

distance from the equator to either pole

• Distance light travels in 1/299,792,458th of a second (c is constant everywhere in the universe)

Historical Pt-Ir meter bars

Kilogram

• Pt-Ir cylinder at the International Bureau of Weights and Measures.

• Rest mass of 6.022 X 10

U.S. National Kilogram (NIST)

Second

• 1/86,400 of a mean solar day

• Defined in terms of frequency of radiation emitted by a cesium isotope

Cesium Fountain Clock at NIST

Giga (G) = 109

Mega (M) = 106

kilo (k) = 103

hecto (h) = 102

deka (da) = 101

deci (d) = 10-1

centi (c) = 10-2

milli (m) = 10-3

micro () = 10-6

nano (n) = 10-9

pico (p) = 10-12

Examples:

1 km = 1 X 103 m

450 km = 450 X 103 m = 4.5 X 105 m

45 uF = 45 X 10-6 F = 4.5 X 10-5 F

The Metric System

Examples:

600 nm = ? m

0.0055 Gs = ? s

5677 kg = ? g

The Metric System

Examples:

600 nm = 6 X 10-7 m

0.0055 Gs = 5.5 X 106 s

0.000567 kg = 5.67 X 10-1 g

The Metric System

Metric Example One:

How many meters is 55 cm?

Step 1: 55 cmStep 2: 55 cm X m

cmStep 3: 55 cm X 1 X 10-2 m

1 cmStep 4: 55 cm X 1 X 10-2 m = 0.55 m

1 cm ALWAYS include this zero

Metric Example 2:

How many milliters is 0.0250 liters?

Step 1: 0.0250 LStep 2: 0.0250 L mL

LStep 3: 0.0250 L 1 mL

1 X 10-3 LStep 4: 0.0250 L 1 mL = 25.0 mL

1 X 10-3 L

Metric Example 3

How many kilograms is 13405 mg?

13405 mg 1 X 10-3 g

1 mg

13405 mg 1 X 10-3 g 1 kg

1 mg 1 X 103 g

13405 mg 1 X 10-3 g 1 kg = 0.013405 kg

1 mg 1 X 103 g

Metric Example 4

How many milliseconds is 0.0450 hectoseconds?

(Ans: 4500 ms)

4658 cm = ? km635 cm = ? dam553 ms = ? ds0.0023 kL = ? mL0.468 cm = ? mm7200 cs = ? das3498 s = ? hours

Metric Practice Examples

4658 cm = 0.04658 km635 cm = 0.635 dam553 ms = 5.53 ds0.0023 kL = 2300 mL0.468 cm = 4.68 mm7200 cs = 7.2 das3498 s = 0.9717 hours

Metric Practice Examples

Metric Example 5

How many square meters is 685 cm2?685 cm2 1 X 10-2 m

1 cm

685 cm2 1 X 10-2 m 1 X 10-2 m1 cm 1 cm

685 cm2 1 X 10-2 m 1 X 10-2 m = 0.0685 m2

1 cm 1 cm

Metric Example 6

How many square decimeters is 0.250 m2?0.250 m2 1 dm

1X10-1 m

0.250 m2 1 dm 1 dm 1X10-1 m 1X10-1 m

0.250 m2 1 dm 1 dm = 25.0 dm2

1X10-1 m 1X10-1 m

Metric Example 7

How many cubic centimeters (cm3) is 0.00453 m3?

(Ans: 4520 cm3)

Challenge Problem

The tallest building in the world is in Taiwan, Taipei 101. It is 509 meters tall. How many feet is that?

(1 cm = 2.54 inches)

http://en.wikipedia.org/wiki/Image:Taipei_101_International_Finadnc

ial_Center.jpg

Metric Example 9

Convert 22 miles/hour to m/s.

This problem will require us to do two things: convert the distances and convert the time.

22 miles 1.61 km 1X103m 1 hr 1 min = 9.8 m/s

1 hr 1.00 mile 1 km 60 min 60 s

Metric Example 10

Convert 200 cm/s to miles/hour.

200 cm 1X10-2 m 1 km 1.00 mile 60 s 60 min

1 s 1 cm 1X103 m 1.61 km 1 min 1 hr

= 4.47 miles/hr

55 mi/hr km/hr

55 mi/hr meters/min

65 miles/hr meters/s

400 cm/s miles/hr

Metric Practice Examples

55 mi/hr 89 km/hr

55 mi/hr 1476 meters/min

65 miles/hr 29.1 meters/s

400 cm/s 8.94 miles/hr

Metric Practice Examples

Accuracy and Precision

• Accuracy– how close the average of a set of measurements

is to the true value– Measured using Percent Error

• Precision– How close a set of measured values are to one

another– Measured using Range

Accuracy and Precision

Students did trials to measure the density of a metal. The accepted density is 7.2 g/cm3. Were they accurate or precise?

Set 1 7.21 7.25 7.18

Set 2 6.40 7.90 7.30

Set 3 6.45 6.52 6.48

Percent Error – Measure of accuracy

% Error = Experimental – Accepted X 100Accepted

NOTE: The “Experimental” value is always the average of all your trials in an experiment

Error Analysis

A student measures the density of a sample of copper and determines it to be 8.75 g/mL. The accepted value is 8.96 g/mL. Calculate the percent error.

Error Analysis: Example 1

A student measures the melting point of a sample of beryllium at 667 oC. The accepted value is 649 oC. Calculate the percent error.

Error Analysis: Example 2

Error Analysis: Range

Range - Measure of precision

Range = highest trial – lowest trial

Example 1A student measures the melting point of a

sample of beryllium and does four trials. The trials result in melting points of 667 oC, 645 oC, 670 oC, 655 oC. Calculate the range and comment on precision.

Error Analysis: Range

Example 2

A student measures the density of a sample of lead and does four trials. The trials result in densities of 11.3, 10.5, 11.9, 10.8 g/cm3. Calculate the range and comment on precision.

Error Analysis

Example 3

Using the numbers in the previous example, calculate percent error. The accepted density of lead is 11.4 g/cm3.