Dimensional Analysis Metric System. Let’s look at the chart again

Dimensional Analysis

Metric System

Let’s look at the chart again.


Meter, Liter, GramStandard Unit SI


Kilo

Kilo comes the Greek word meaning “thousand”

So we use this word and prefix to indicate that there are a thousand of the SI unit in one Kilo

EXAMPLE: 1000m = 1 km1000 L = 1 kL1000g = 1kg


Centi

• Centi comes the latin word meaning “hundred”

• Think of a Penny. One hundred pennies makes a dollar.

• 100 years makes a century• In dimensional analysis, a centi is SMALLER

than the SI unit.

Centi

• 100 cm = 1m• 100 cg = 1 g• 100 cL = 1 L


milli

• Latin word for “thousand”• Millipede (one thousand, pedis means foot)• A milli is smaller than the SI unit

• 1000 mL = 1L• 1000 mg = 1g• 1000 mm = 1m

• EX. How many meter are in 925 km?

925 km ? m=

Draw the dimensional “jumps”.

925 km ? m=

925 km x

* Use charts or tables to find relationships

Insert relationship so units cancel.

925 km xkm

*units of known in denominator (bottom) first*** units of unknowns in numerator (top

m

1

1,000

Cancel units

925 km xkm

m

1

1,000

Do the Math

925 km xkm

m

1

1,000

1 x 1=

925 x 1,000

1=

925,000= 925,000

How wide is our universe?

210,000,000,000,000,000,000,000 miles(22 zeros)

This number is written in decimal notation. When numbers get this large, it is easier to write them in

scientific notation.

Scientific Notation

A number is expressed in scientific notation when it is in the form

a x 10n

where a is between 1 and 10

and n is an integer

Write the width of the universe in scientific notation.

210,000,000,000,000,000,000,000 miles

Where would you put the decimal to make this number be between 1 and

10?

2.10,000,000,000,000,000,000,000.

How many decimal places did you move the decimal?

2.10,000,000,000,000,000,000,000.


23

2.10,000,000,000,000,000,000,000.


23When the original number is more than 1,

the exponent is positive.The answer in scientific notation is

2.10,000,000,000,000,000,000,000.


23When the original number is more than 1,

the exponent is positive.The answer in scientific notation is

2.1 x 1023

1) Express 0.0000000902 in scientific notation.

Where would the decimal go to make the number be between 1 and 10?



9.02



9.02The decimal was moved how many places?




8




8When the original number is less than 1, the

exponent is negative.




8When the original number is less than 1, the

exponent is negative.9.02 x 10-8

LecturePLUS Timberlake 31

Learning Check

How many seconds are in 1.4 days?

Unit plan: days hr min seconds

1.4 days x 24 hr x ?? 1 day

LecturePLUS Timberlake 32

Solution

Unit plan: days hr min seconds

1.4 day x 24 hr x 60 min x 60 sec 1 day 1 hr 1 min

= 1.2 x 105 sec

Accuracy versus Precision

• Accuracy: how close you are to the actual value

• Precision: the ability to measure with exactness, repeatability.


• VALUES IN DATA: • 12.33 cm• 12.21 cm• 12.27 cm• 12.24 cm

• ACTUAL VALUE: 99 cm

The data is precise, but not accurate


• VALUES IN DATA:• 95.89 cm• 101.22 cm• 96.80 cm• 99.2 cm


The data is accurate but not precise


• VALUES OF DATA:• 14.53 cm• 99.49 cm• 57.90 cm• 32.84 cm


The data neither accurate nor precise


• VALUES OF DATA:• 99.87 cm• 99.12 cm• 98.99 cm• 99.53 cm


The data is both accurate and precise.

CALCULATING DEGREE OF ERROR

• Measurement – Actual Value X 100 Actual Value

EX: measurement is 29. Actual Value is 27.5

29 – 27.5 X 100 = 5.45% percentage of error 27.5

OTHER MEASUREMENTS

• VOLUME = L , cm3, cc• MASS= g• LENGTH= m• DENSITY = g/ml, g/cm3

LET’S REVIEW

The student determines that the unknown substance is sodium chloride. Which of the following is an extensive property of sodium chloride?•Mass of 15 g•White color•Density of 2.17 g/cm3

• Solubility in water19.

The safest way to dilute concentrated sulfuric acid is to add:

– A series of small volumes of water to the acid while stirring.

– The acid to water slowly while stirring constantly.– The acid to a small volume of water and then add

more water.– Dilute sulfuric acid to a small volume of the

concentrated acid.

• WHAT HAPPENED TO THE DENSITY OF THE SUBSTANCE???

What is the most appropriate unit of measure for reporting the density of a solid?

– g/cm3

– g/cm– g/L2

– g/mm2

Volume is space the matter takes up

cm3 = cc = mL

• These are the measurements of volume.

• The METRIC measurement for VOLUME is mL

• There will be at least three questions when you will need to know this.

Jeremy decides to cook some pasta noodles. He notices that the directions say to add salt to water before bringing it to a

boil. The next day, Jeremy asks his science teacher, Ms. Jackson, a question: “How does adding salt affect the way water boils?” Ms. Jackson then asks Jeremy to plan and

conduct an experiment to find the answer. The following graph summarizes Jeremy’s results. Which list of materials

and equipment best represents what Jeremy would have used in order to get these results?

• Beaker, water, pasta, table salt, pipette, hot plate, measuring spoon.

• Beaker, water, pasta, table salt, pH meter, hot plate, spatula, ring stand.

• Beaker, water, pasta, table salt, thermometer, hot plate, timer, ice cubes.

• Beaker, water, pasta, table salt, thermometer, hot plate, spatula, balance.

Which of the following pieces of equipment would be most appropriate for measuring the volume of a marble?

How many significant figures

• 32.983• 8.000• 4839.4• 0.000000000000023• 23,000.0• 450,057

What do these PREFIXES mean

• Kilo• Centi• Milli

KILO

• Greek for ‘thousand’• Means 1000 times larger

Centi

• Latin for ‘hundred’• Mean 100 times SMALLER

milli

• Latin for ‘thousand’• Means 1000 times smaller

Temperature Conversions

Ko= Co + 273 Co = Ko - 273Fo = 9/5 (Co +32) Co = 5/9 (Fo-32)

WHAT YOU’RE GIVEN ON THE STAAR EXAM AND TAKS

0 Co = 273 Ko

Precision and Accuracy

Team 1- 2.65 cm Team 2 - 2.75 cm Team 3 - 2.80 cmTeam 4 - 2.77 cm ACTUAL MEASUREMENTTeam 5 - 2.77 cm 2.70 cm Team 6 - 2.65 cm

Accurate, precise, both or neither

Percentage of Error

• Measurement – actual value X 100 = %

actual measurement

EXAMPLE: team 1 2.65

2.65 – 2.70 X 100 = 1.85 % 2.70

The quantitative measurement among the following is:

– The oak tree is taller than the maple.– The oak tree is very tall.– The oak tree is 15 meters tall.– The oak tree is taller than the house.

•

Study Well

• Belief is half the battle. Good Luck

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Dimensional Analysis Metric System. Let’s look at the chart again