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# Chapter 3: Scientific Measurement

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Tweet## Eric Valuyev

on 18 September 2012#### Transcript of Chapter 3: Scientific Measurement

Chapter 3: Scientific Measurement 3.1: Measurements and Their Uncertainty 3.2: The International System of Units 3.3: Conversion Problems A Measurement is a quantity that has both a number and unit.

In Scientific Notation, a given number written as the product of two numbers: a coefficient and 10 raised to a power. (Ex. 294,000,000=2.94 x 108)

Accuracy is the measure of how close a measurement comes to the actual or true value of whatever is measure.

Precision is a measure of how close a series of measurements are to one another.

The Accepted Value is the correct value based on reliable reference.

The Experimental Value is the value measured in a lab.

The Error is the difference between the experimental value and the accepted value. (Error = Experimental Value – Accepted Value)

The Percent Error is the absolute value of the error divided by the accepted value, multiplied by 100%. (Percent Error = (|Error|/Accepted Value) x 100%)

Significant Figures in a measurement are all of the digits that are known, plus a last estimated digit. •Measurements are fundamental to the experimental sciences. For that reason, it is important to be able to make measurements and to decide whether a measurement is correct.

•To evaluate the accuracy of a measurement, the measured value must be compared to the correct value. To evaluate the precision of a measurement, you must compare the values of two or more repeated measurements.

•Measurements must always be reported to the correct number of significant figures because calculated answers often depend on the number of significant figures in the value used in the calculation.

•In general, a calculated answer cannot be more precise than the least precise measurement from which it is calculated. A measurement always has some degree of uncertainty. Significant figures are the meaningful figures in our measurements and they allow us to generate meaningful conclusions

Numbers recorded in a measurement are significant.

All the certain numbers plus first estimated number

e.g. 2.85 cm

We need to be able to combine data and still produce meaningful information

There are rules about combining data that depend on how many significant figures we start with……… Significant Figures Vocabulary Key Concepts 1. Nonzero integers always count as significant figures.

1457 (4 significant figures)

23.3 (3 significant figures)

2. Zeros

Leading zeros - never count

0.0025 (2 significant figures)

Captive zeros - always count

1.008 (4 significant figures)

Trailing zeros - count only if the number is written with a decimal point

100 (1 significant figure)

100. (3 significant figures)

120.0 (4 significant figures) Rules for Counting Significant Figures 102

102.0

1.02

12000

120.02

0.00102

0.10200 1422

65,321

1.004 x 105

200

435.662

50.041

1,234,567.89 How Many Significant Figures? 1. The number of significant figures in the result is the same as in the measurement with the smallest number of significant figures. Rules for Multiplication and Division 2. The number of significant figures in the result is the same as in the measurement with the smallest number of decimal places. Rules for Addition and Subtraction 50 cm + 150 cm = 200 cm Addition / Subtraction

When you Add or Subtract measurements they must be in the same units and the units remain the same 50 cm x 150 cm = 7500 cm2

20 m / 5 s = 4 m/s or 4 ms-1

16m / 4m = 4 Multiplication / Division

When you Multiply or Divide measurements you must carry out the same operation with the units as you do with the numbers Rules for Combined Units 11.7 km x 15.02 km =

12 mm x 34 mm x 9.445 mm =

14.05 m / 7 s =

108 kg / 550 m3 =

23.2 L + 14 L =

55.3 s + 11.799 s =

16.37 cm – 4.2 cm =

350.55 km – 234.348 km = Calculate the following. Give your answer to the correct number of significant figures and use the correct units - Round off 52.394 to 1,2,3,4 significant figures Calculating the Error of an Experiment

Accepted Value = 9.57 Experimental Value = 10.00

Error = 10.00-9.57

Error = 0.43 Calculating the % Error of an Experiment

% Error = (|0.43| / 9.57) x 100%

% Error = 4.49% 3. Exact Numbers - unlimited significant figures

4. Not obtained by measurement

Determined by counting: 3 apples

Determined by definition: 1 in. = 2.54 cm

The International System of Units (SI) is a revised version of the metric system.

The Meter (m) is the basic unit of length, or linear measure.

A Liter (L) is the volume of a cube that is 10 centimeters along each edge (10cm x 10cm x 10cm = 1000cm3 = 1L)

A Kilogram (kg) is the basic SI unit of mass which is used to measure the comparison of the mass of another object.

A Gram (g) is 1/1000 of a kilogram; the mass of 1cm3 of water at 4°C is 1g.

Weight is the force that measures the pull on a given mass by gravity.

Temperature is a measure of how hot or cold an object is.

The Celsius Scale sets the freezing point of water at 0°C and the boiling point of water at 100°C.

On the Kelvin Scale, the freezing point of water is 273.15 K, and the boiling point is 373.15 K.

Absolute Zero is the 0 K point on the Kelvin scale and is equal to -273.15°C which is usually rounded to -273°C along with all other computation between Celsius and Kelvin.

Energy is the capacity to do work or to produce heat.

The Joule (J) is the SI unit of energy.

One Calorie (cal) is the quantity of heat that raises the temperature of 1g of pure water to 1°C.

•The five SI base units commonly used by chemists are the meter, the kilogram, the kelvin, the second, and the mole.

•Common metric units of length include the centimeter, meter, and kilometer.

•Common metric units of volume include the liter, milliliter, cubic centimeter, and microliter.

•Common metric units of mass include the kilogram, gram, milligram, and microgram.

•Scientists commonly use two equivalent units of temperature, the degree Celsius and the kelvin.

•The joule and the calorie are common units of energy. Key Concepts Vocabulary Kelvin = Celsius + 273.15 degrees Ex. The average body temperature is 37 degrees Celsius. What is the human body temperature in Kelvin?

37 deg. C + 273 deg. (can round conversion to nearest whole #) = 310 K

A Conversion Factor is a ratio of equivalent measurements.

Dimensional Analysis is a way to analyze and solve problems using units, or dimensions, of the measurements.

•When a measurement is multiplied by a conversion factor, the numerical value is generally changed, but the actual size of the quantity measured remains the same.

•Dimensional analysis provides you with an alternative approach to problem solving.

•Problems in which a measurement with one unit is converted to an equivalent measurement with another unit are easily solved using dimensional analysis. Vocabulary

Key Concepts There are many different ways to express the same amount.

100 pennies = 1 dollar

12 eggs = 1 dozen

1 meter = 100 centimeters

Conversion Factors show these equal numbers as a ratio. Conversion Factors 100 pennies or 1 dollar

1 dollar 100 pennies

12 eggs or 1 dozen

1 dozen 12 eggs

1 meter or 100 centimeters

100 centimeters 1 meter For example, 100 pennies = 1 dollar.

If I have 4.38 dollars, that is the same as having 438 pennies.

You know this from great practice growing up, but how did you do that calculation?

4.38 dollars x 100 pennies = 438 pennies

1 1 dollar Both 4.38 dollars and 438 pennies are the same amount of money, just expressed differently using different units.

Multiplying or diving by a conversion factor is just like multiplying or dividing by 1. The amount may look different with different units, but it still is equal to the original amount. If a farmer has 3 dozen eggs, how many individual eggs does he have?

3 dozen x 12 eggs = 36 eggs

1 1 dozen

3 dozen and 36 eggs are the same amount of eggs, just expressed differently with different units. Example Dimensional Analysis is a way to analyze and solve problems using the units of the measurements.

This is what we use with conversion factors.

You use this all the time without knowing it! Dimensional Analysis Your school club sold 600 tickets to a chili dinner fundraiser. You volunteered to help make the chili. The recipe you have serves 10 people, and calls for 2 tsp of chili powder. How much chili powder do you need for 600 people? Dimensional Analysis Example What do we know?

Servings = 600

10 servings = 2 tsp chili powder means:

10 servings or 2 tsp chili powder

2 tsp chili powder 10 servings

What do we not know?

Amount of chili powder = ? Tsp

What is our plan?

Use conversion to solve for the amount of chili

powder needed. Step 1: Analyze You have 600 servings to make, but your answer needs to be in tsp of chili powder. This means you want the “servings” unit to cancel out and go away.

This means you want to pick the conversion factor with servings in the denominator, making servings cancel.

600 servings x 2 tsp powder = 120 tsp chili powder

1 10 servings Step 2: Calculate The question asked for an amount of chili powder in tsp.

You found you need 120 tsp of chili powder.

You answered the question.

Good Job! Step 3: Evaluate 3.4: Density

Density is the ratio of the mass of an object to its volume.

•Density is an intensive property that depends only on the composition of a substance, not the size of the sample.

•The density of a substance generally decreases as its temperature increases. Vocabulary

Key Concepts If you take the same volume of different substances, then they will weigh different amounts. Density is the Mass per unit Volume What is Density? d = m/V m V Density Equation: g cm-3 or k gm-3 cm3 or kg3 g or kg Volume Mass Density = d g/cm3 Aluminium 2.70 Iron 7.86 Brass 8.50 Wood 0.50 Slate 2.90 Glass 2.50 Density of Common Elements/Compounds Find the mass of the solid on a balance.

Add water until just overflowing.

Place a Measuring Cylinder under the spout.

Add the Object.

Collect the Water and read off the Volume.

Calculate Density DENSITY OF AN IRREGULAR SOLID Find the Mass of the solid on a balance.

Fill the Measuring Cylinder with Water to a known Volume.

Add the Object.

Work out the Volume of Water that is displaced.

Calculate the Density. Find the Mass of an empty Measuring Cylinder.

Add a certain Volume of Liquid.

Find the Mass of the Measuring Cylinder and Liquid

Calculate the Mass of Liquid.

How?

Calculate Density of Liquid. DENSITY OF A LIQUID Remove the air from a flask of a known Volume, using a vacuum pump.

Find its Mass.

Add the gas to be tested.

Reweigh.

The difference is the Mass of gas.

Calculate Density. DENSITY OF A GAS OR That's All You Need To Know For Chapter 3!

Full transcriptIn Scientific Notation, a given number written as the product of two numbers: a coefficient and 10 raised to a power. (Ex. 294,000,000=2.94 x 108)

Accuracy is the measure of how close a measurement comes to the actual or true value of whatever is measure.

Precision is a measure of how close a series of measurements are to one another.

The Accepted Value is the correct value based on reliable reference.

The Experimental Value is the value measured in a lab.

The Error is the difference between the experimental value and the accepted value. (Error = Experimental Value – Accepted Value)

The Percent Error is the absolute value of the error divided by the accepted value, multiplied by 100%. (Percent Error = (|Error|/Accepted Value) x 100%)

Significant Figures in a measurement are all of the digits that are known, plus a last estimated digit. •Measurements are fundamental to the experimental sciences. For that reason, it is important to be able to make measurements and to decide whether a measurement is correct.

•To evaluate the accuracy of a measurement, the measured value must be compared to the correct value. To evaluate the precision of a measurement, you must compare the values of two or more repeated measurements.

•Measurements must always be reported to the correct number of significant figures because calculated answers often depend on the number of significant figures in the value used in the calculation.

•In general, a calculated answer cannot be more precise than the least precise measurement from which it is calculated. A measurement always has some degree of uncertainty. Significant figures are the meaningful figures in our measurements and they allow us to generate meaningful conclusions

Numbers recorded in a measurement are significant.

All the certain numbers plus first estimated number

e.g. 2.85 cm

We need to be able to combine data and still produce meaningful information

There are rules about combining data that depend on how many significant figures we start with……… Significant Figures Vocabulary Key Concepts 1. Nonzero integers always count as significant figures.

1457 (4 significant figures)

23.3 (3 significant figures)

2. Zeros

Leading zeros - never count

0.0025 (2 significant figures)

Captive zeros - always count

1.008 (4 significant figures)

Trailing zeros - count only if the number is written with a decimal point

100 (1 significant figure)

100. (3 significant figures)

120.0 (4 significant figures) Rules for Counting Significant Figures 102

102.0

1.02

12000

120.02

0.00102

0.10200 1422

65,321

1.004 x 105

200

435.662

50.041

1,234,567.89 How Many Significant Figures? 1. The number of significant figures in the result is the same as in the measurement with the smallest number of significant figures. Rules for Multiplication and Division 2. The number of significant figures in the result is the same as in the measurement with the smallest number of decimal places. Rules for Addition and Subtraction 50 cm + 150 cm = 200 cm Addition / Subtraction

When you Add or Subtract measurements they must be in the same units and the units remain the same 50 cm x 150 cm = 7500 cm2

20 m / 5 s = 4 m/s or 4 ms-1

16m / 4m = 4 Multiplication / Division

When you Multiply or Divide measurements you must carry out the same operation with the units as you do with the numbers Rules for Combined Units 11.7 km x 15.02 km =

12 mm x 34 mm x 9.445 mm =

14.05 m / 7 s =

108 kg / 550 m3 =

23.2 L + 14 L =

55.3 s + 11.799 s =

16.37 cm – 4.2 cm =

350.55 km – 234.348 km = Calculate the following. Give your answer to the correct number of significant figures and use the correct units - Round off 52.394 to 1,2,3,4 significant figures Calculating the Error of an Experiment

Accepted Value = 9.57 Experimental Value = 10.00

Error = 10.00-9.57

Error = 0.43 Calculating the % Error of an Experiment

% Error = (|0.43| / 9.57) x 100%

% Error = 4.49% 3. Exact Numbers - unlimited significant figures

4. Not obtained by measurement

Determined by counting: 3 apples

Determined by definition: 1 in. = 2.54 cm

The International System of Units (SI) is a revised version of the metric system.

The Meter (m) is the basic unit of length, or linear measure.

A Liter (L) is the volume of a cube that is 10 centimeters along each edge (10cm x 10cm x 10cm = 1000cm3 = 1L)

A Kilogram (kg) is the basic SI unit of mass which is used to measure the comparison of the mass of another object.

A Gram (g) is 1/1000 of a kilogram; the mass of 1cm3 of water at 4°C is 1g.

Weight is the force that measures the pull on a given mass by gravity.

Temperature is a measure of how hot or cold an object is.

The Celsius Scale sets the freezing point of water at 0°C and the boiling point of water at 100°C.

On the Kelvin Scale, the freezing point of water is 273.15 K, and the boiling point is 373.15 K.

Absolute Zero is the 0 K point on the Kelvin scale and is equal to -273.15°C which is usually rounded to -273°C along with all other computation between Celsius and Kelvin.

Energy is the capacity to do work or to produce heat.

The Joule (J) is the SI unit of energy.

One Calorie (cal) is the quantity of heat that raises the temperature of 1g of pure water to 1°C.

•The five SI base units commonly used by chemists are the meter, the kilogram, the kelvin, the second, and the mole.

•Common metric units of length include the centimeter, meter, and kilometer.

•Common metric units of volume include the liter, milliliter, cubic centimeter, and microliter.

•Common metric units of mass include the kilogram, gram, milligram, and microgram.

•Scientists commonly use two equivalent units of temperature, the degree Celsius and the kelvin.

•The joule and the calorie are common units of energy. Key Concepts Vocabulary Kelvin = Celsius + 273.15 degrees Ex. The average body temperature is 37 degrees Celsius. What is the human body temperature in Kelvin?

37 deg. C + 273 deg. (can round conversion to nearest whole #) = 310 K

A Conversion Factor is a ratio of equivalent measurements.

Dimensional Analysis is a way to analyze and solve problems using units, or dimensions, of the measurements.

•When a measurement is multiplied by a conversion factor, the numerical value is generally changed, but the actual size of the quantity measured remains the same.

•Dimensional analysis provides you with an alternative approach to problem solving.

•Problems in which a measurement with one unit is converted to an equivalent measurement with another unit are easily solved using dimensional analysis. Vocabulary

Key Concepts There are many different ways to express the same amount.

100 pennies = 1 dollar

12 eggs = 1 dozen

1 meter = 100 centimeters

Conversion Factors show these equal numbers as a ratio. Conversion Factors 100 pennies or 1 dollar

1 dollar 100 pennies

12 eggs or 1 dozen

1 dozen 12 eggs

1 meter or 100 centimeters

100 centimeters 1 meter For example, 100 pennies = 1 dollar.

If I have 4.38 dollars, that is the same as having 438 pennies.

You know this from great practice growing up, but how did you do that calculation?

4.38 dollars x 100 pennies = 438 pennies

1 1 dollar Both 4.38 dollars and 438 pennies are the same amount of money, just expressed differently using different units.

Multiplying or diving by a conversion factor is just like multiplying or dividing by 1. The amount may look different with different units, but it still is equal to the original amount. If a farmer has 3 dozen eggs, how many individual eggs does he have?

3 dozen x 12 eggs = 36 eggs

1 1 dozen

3 dozen and 36 eggs are the same amount of eggs, just expressed differently with different units. Example Dimensional Analysis is a way to analyze and solve problems using the units of the measurements.

This is what we use with conversion factors.

You use this all the time without knowing it! Dimensional Analysis Your school club sold 600 tickets to a chili dinner fundraiser. You volunteered to help make the chili. The recipe you have serves 10 people, and calls for 2 tsp of chili powder. How much chili powder do you need for 600 people? Dimensional Analysis Example What do we know?

Servings = 600

10 servings = 2 tsp chili powder means:

10 servings or 2 tsp chili powder

2 tsp chili powder 10 servings

What do we not know?

Amount of chili powder = ? Tsp

What is our plan?

Use conversion to solve for the amount of chili

powder needed. Step 1: Analyze You have 600 servings to make, but your answer needs to be in tsp of chili powder. This means you want the “servings” unit to cancel out and go away.

This means you want to pick the conversion factor with servings in the denominator, making servings cancel.

600 servings x 2 tsp powder = 120 tsp chili powder

1 10 servings Step 2: Calculate The question asked for an amount of chili powder in tsp.

You found you need 120 tsp of chili powder.

You answered the question.

Good Job! Step 3: Evaluate 3.4: Density

Density is the ratio of the mass of an object to its volume.

•Density is an intensive property that depends only on the composition of a substance, not the size of the sample.

•The density of a substance generally decreases as its temperature increases. Vocabulary

Key Concepts If you take the same volume of different substances, then they will weigh different amounts. Density is the Mass per unit Volume What is Density? d = m/V m V Density Equation: g cm-3 or k gm-3 cm3 or kg3 g or kg Volume Mass Density = d g/cm3 Aluminium 2.70 Iron 7.86 Brass 8.50 Wood 0.50 Slate 2.90 Glass 2.50 Density of Common Elements/Compounds Find the mass of the solid on a balance.

Add water until just overflowing.

Place a Measuring Cylinder under the spout.

Add the Object.

Collect the Water and read off the Volume.

Calculate Density DENSITY OF AN IRREGULAR SOLID Find the Mass of the solid on a balance.

Fill the Measuring Cylinder with Water to a known Volume.

Add the Object.

Work out the Volume of Water that is displaced.

Calculate the Density. Find the Mass of an empty Measuring Cylinder.

Add a certain Volume of Liquid.

Find the Mass of the Measuring Cylinder and Liquid

Calculate the Mass of Liquid.

How?

Calculate Density of Liquid. DENSITY OF A LIQUID Remove the air from a flask of a known Volume, using a vacuum pump.

Find its Mass.

Add the gas to be tested.

Reweigh.

The difference is the Mass of gas.

Calculate Density. DENSITY OF A GAS OR That's All You Need To Know For Chapter 3!