Dimensional Analysis Metric System

Let’s look at the chart again.

Meter, Liter, GramStandard Unit SI

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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 km 1000 L = 1 kL 1000g = 1kg

Let’s look at the chart again.

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

Let’s look at the chart again.

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 kmx * Use charts or tables to find relationships

Insert relationship so units cancel. 925 km x km *units of known in denominator (bottom) first *** units of unknowns in numerator (top m 1 1,000

Cancel units 925 kmx km m 1 1,000

Do the Math 925 kmx km m 1 1,000 1 x 1 = 925 x 1,000 1 = 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 10 n 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. How many decimal places did you move the decimal? 23

2. 10,000,000,000,000,000,000,000. How many decimal places did you move the decimal? 23 When 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. How many decimal places did you move the decimal? 23 When the original number is more than 1, the exponent is positive. The answer in scientific notation is 2.1 x 10 23

1) Express in scientific notation. Where would the decimal go to make the number be between 1 and 10?

1) Express in scientific notation. Where would the decimal go to make the number be between 1 and 10? 9.02

1) Express in scientific notation. Where would the decimal go to make the number be between 1 and 10? 9.02 The decimal was moved how many places?

1) Express in scientific notation. Where would the decimal go to make the number be between 1 and 10? 9.02 The decimal was moved how many places? 8

1) Express in scientific notation. Where would the decimal go to make the number be between 1 and 10? 9.02 The decimal was moved how many places? 8 When the original number is less than 1, the exponent is negative.

1) Express in scientific notation. Where would the decimal go to make the number be between 1 and 10? 9.02 The decimal was moved how many places? 8 When the original number is less than 1, the exponent is negative x 10 -8

LecturePLUS Timberlake31 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 Timberlake32 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 10 5 sec

Accuracy versus Precision Accuracy: how close you are to the actual value Precision: the ability to measure with exactness, repeatability.

Accuracy versus Precision VALUES IN DATA: cm cm cm cm ACTUAL VALUE: 99 cm The data is precise, but not accurate

Accuracy versus Precision VALUES IN DATA: cm cm cm 99.2 cm ACTUAL VALUE: 99 cm The data is accurate but not precise

Accuracy versus Precision VALUES OF DATA: cm cm cm cm ACTUAL VALUE: 99 cm The data neither accurate nor precise

Accuracy versus Precision VALUES OF DATA: cm cm cm cm ACTUAL VALUE: 99 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 X 100 = 5.45% percentage of error 27.5

OTHER MEASUREMENTS VOLUME = L, cm 3, cc MASS= g LENGTH= m DENSITY = g/ml, g/cm 3

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/cm 3 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/cm 3 – g/cm – g/L 2 – g/mm 2

Volume is space the matter takes up

cm 3 = 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 , ,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 K o = C o C o = K o F o = 9/5 (C o +32) C o = 5/9 (F o -32) WHAT YOU’RE GIVEN ON THE STAAR EXAM AND TAKS 0 C o = 273 K o

Precision and Accuracy Team cm Team cm Team cm Team cm ACTUAL MEASUREMENT Team cm 2.70 cm Team cm Accurate, precise, both or neither

Percentage of Error Measurement – actual value X 100 = % actual measurement EXAMPLE: team – 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