Mediciones, Problemas de Conversión y Notación Científica

1

Chapter 2 Measurements

2.1

Units of Measurement

Copyright © 2008 by Pearson Education, Inc.Publishing as Benjamin Cummings

2

Measurement

You make a measurement

every time you• Measure your height. • Read your watch.• Take your temperature.• Weigh a cantaloupe.


3

Measurement

In a measurement

• A measuring tool is used to compare some dimension of an object to a standard.

• Of the thickness of the skin fold at the waist, calipers are used.


4

Stating a Measurement

In a measurement, a number is followed by a unit.

Observe the following examples of measurements:

Number Unit

35 m

0.25 L

225 kg

3.4 hr

5

The Metric System (SI)

The metric system or SI (international system) is

• A decimal system based on 10.

• Used in most of the world.

• Used everywhere by scientists.

6

Units in the Metric System

In the metric (SI) system, one unit is used for each

type of measurement:

Measurement Metric SI

length meter (m) meter (m)

volume liter (L) cubic meter (m3)

mass gram (g) kilogram (kg)

time second (s) second (s)

temperature Celsius (C) Kelvin (K)

11

For each of the following, indicate whether the unit describes 1) length, 2) mass, or 3) volume.

____ A. A bag of onions has a mass of 2.6 kg.

____ B. A person is 2.0 m tall.

____ C. A medication contains 0.50 g aspirin.

____ D. A bottle contains 1.5 L of water.

Learning Check

12

For each of the following, indicate whether the unit describes 1) length, 2) mass, or 3) volume.

2 A. A bag of onions has a mass of 2.6 kg.

1 B. A person is 2.0 m tall.

2 C. A medication contains 0.50 g aspirin.

3 D. A bottle contains 1.5 L of water.

Solution

13

Learning Check Identify the measurement with an SI unit. A. John’s height is

1) 1.5 yd 2) 6 ft 3) 2.1 m

B. The race was won in1) 19.6 s 2) 14.2 min 3) 3.5 hr

C. The mass of a lemon is1) 12 oz 2) 0.145 kg 3) 0.6 lb

D. The temperature is1) 85C 2) 255 K 3) 45F

14

Solution Identify the measurement with an SI unit. A. John’s height is

3) 2.1 m

B. The race was won in1) 19.6 s

C. The mass of a lemon is2) 0.145 kg

D. The temperature is2) 255 K

15

STEP 1 State the given and needed units.

STEP 2 Write a plan to convert the given unit to the

needed unit.

STEP 3 Write equalities/conversion factors that connect the units.

STEP 4 Set up problem with factors to cancel

units and calculate the answer.

Unit 1 x Unit 2 = Unit 2Unit 1

Given Conversion Needed unit factor unit

Guide to Problem Solving (GPS)

16

Setting up a Problem

How many minutes are 2.5 hours?

given unit = 2.5 hr

needed unit = ? min

plan = hr min

Set up problem to cancel units (hr).

given conversion needed unit factor unit

2.5 hr x 60 min = 150 min

1 hr


17

A rattlesnake is 2.44 m long. How long is the snake

in centimeters?

1) 2440 cm

2) 244 cm

3) 24.4 cm

Learning Check

18

A rattlesnake is 2.44 m long. How long is thesnake in centimeters?

2) 244 cm

given conversion needed unit factor unit

2.44 m x 100 cm = 244 cm 1 m

Solution

19

• Often, two or more conversion factors are required to obtain the unit needed for the answer.

Unit 1 Unit 2 Unit 3

• Additional conversion factors can be placed in the setup to cancel each preceding unitGiven unit x factor 1 x factor 2 = needed unitUnit 1 x Unit 2 x Unit 3 = Unit 3

Unit 1 Unit 2

Using Two or More Factors

20

How many minutes are in 1.4 days?

Given unit: 1.4 days Needed unit: min

Plan: days hr min

Equalties: 1 day = 24 hr

1 hr = 60 min Set up problem: 1.4 days x 24 hr x 60 min = 2.0 x 103

min

1 day 1 hr

Example: Problem Solving

21

• Be sure to check your unit cancellation in the setup.

• The units in the conversion factors must cancel to give the correct unit for the answer.

What is wrong with the following setup?1.4 day x 1 day x 1 hr

24 hr 60 min

Units = day2/min is Not the needed unit

Units don’t cancel properly.

Check the Unit Cancellation

More units

Area m2 = m x m Volume m3 = m x m x m Density mass/volume

g/mL or Kg/L

22

K = oC + 273 Ex 23 oC = _______ K 135 K = ________ oC

1L = 1 dm3

1 m3 =1000L

Ex 27 m3 = ________ L23

24

Osmium is a very dense metal. What is its

density in g/cm3 if 50.0 g of osmium has a

volume of 2.22 cm3?

1) 2.25 g/cm3

2) 22.5 g/cm3

3) 111 g/cm3

Learning Check

25

Given: mass = 50.0 g volume = 2.22 cm3

Plan: Write the density expression.

D = mass volume

Express mass in grams and volume in cm3

mass = 50.0 g volume = 2.22 cm3

Set up problem using mass and volume.D = 50.0 g = 22.522522 g/cm3

2.22 cm3

= 22.5 g/cm3

Solution

26

Volume by Displacement

• A solid completely submerged in water displaces its own volume of water.

• The volume of the solid is calculated from the volume difference.45.0 mL - 35.5 mL

= 9.5 mL = 9.5 cm3


27

Density Using Volume Displacement

The density of the object iscalculated from its mass andvolume. mass = 68.60 g = 7.2 g/cm3

volume 9.5 cm3


28

Sink or Float

• Ice floats in water because the density of ice is less than the density of water.

• Aluminum sinks because its density is greater than the density of water.


29

Which diagram correctly represents the liquid layers in the cylinder? Karo (K) syrup (1.4 g/mL), vegetable (V) oil (0.91 g/mL,) water (W) (1.0 g/mL)

1 2 3

K

K

W

W

W

V

V

V

K

Learning Check

30

1)

vegetable oil 0.91 g/mL

water 1.0 g/mL

Karo syrup 1.4 g/mL

K

W

V

Solution

31

Chapter 2 Measurements

2.2

Scientific Notation


32

Scientific NotationScientific notation • Is used to write very large

or very small numbers.• For the width of a human

hair of 0.000 008 m is written as

8 x 10-6 m• For a large number such

as 2 500 000 s is written as

2.5 x 106 s Copyright © 2008 by Pearson Education, Inc.Publishing as Benjamin Cummings

33

Scientific Notation

• A number written in scientific notation contains a coefficient and a power of 10.

coefficient power of ten coefficient power of ten

1.5 x 102 7.35 x 10-4

• To write a number in scientific notation, the decimal point is moved after the first digit.

• The spaces moved are shown as a power of ten.

52 000. = 5.2 x 104 0.00378 = 3.78 x 10-

3

4 spaces left 3 spaces right

34

Some Powers of Ten

Copyright © 2008 by Pearson Education, Inc. Publishing as Benjamin Cummings

35

Comparing Numbers in Standard and Scientific Notation

Number in Standard Format Scientific NotationDiameter of the Earth 12 800 000 m 1.28 x 107 mMass of a human 68 kg 6.8 x 101 kgMass of a hummingbird 0.002 kg 2 x 10-3 kg Length of a pox virus 0.000 000 3 cm 3 x 10-7 cm

36

Learning Check

Select the correct scientific notation for each.

A. 0.000 008

1) 8 x 106 2) 8 x 10-6 3) 0.8 x 10-5

B. 72 000

1) 7.2 x 104 2) 72 x 103 3) 7.2 x 10-4

37

Solution

Select the correct scientific notation for each.

A. 0.000 008

2) 8 x 10-6

B. 72 000

1) 7.2 x 104

38

Learning Check

Write each as a standard number.

A. 2.0 x 10-2

1) 200 2) 0.0020 3) 0.020

B. 1.8 x 105

1) 180 000 2) 0.000 018 3) 18 000

39

Solution

Write each as a standard number.

A. 2.0 x 10-2

3) 0.020

B. 1.8 x 105

1) 180 000

Documents

Mediciones, Problemas de Conversión y Notación Científica