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To Measure

“to measure” means to compare a quantity to a standard unit This is the process of collecting data.

Why is measurement important in science?

Communication: Measurement lets us turn ideas into numbers, which everyone agrees on. Data Analysis: Use graphs and calculations to look for patterns in data. Equations: Get equations to summarize patterns in data and make predictions.

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Quantity

Quantity: what you measure Examples: length, mass, time, temperature

Unit

Unit: how you measure a quantity Examples: length is measured in units of meters (m), inches (in), or feet (ft) mass is measured in units of kilograms (kg) time is measured in units of seconds (s)

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Measuring Instrument

(Tool)

A measuring instrument is what you use to measure a quantity. Examples: Meter stick to measure length Triple-beam balance to measure mass Stopwatch to measure time Thermometer to measure temperature

Why are metric units more convenient than British units?

Metric units are easier to convert from one unit to another. Each metric units is always divided into 10s. Examples: 1 m = 10 mm, 1 m = 100 cm British units have different divisions for different size units. Examples: 1 ft = 12 in, 1 in can be divided into 1/8th of an inch (not 10 parts)

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“Base” Quantities

Basic “Lego” blocks for quantities. Example: Length, Mass, and Time are basic to describing nature. Other quantities, like area and volume, are defined from base quantities.

“Derived” Quantities

“Derived quantities” come from formulas that use base quantities. Example: Volume is a derived quantity from Length (a base quantity) using the formula: V = L x W x H U

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What are 5 common base quantities?

What are 5 common metric base units?

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What are the abbreviations for the 5 common metric base units?

(“abbreviated” = short)

Distance, Width, and Height are the same as which

base quantity?

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Length is the base quantity that is the same as Distance, Width, and Height. You measure Distance, Width, or Height using Length units (e.g., meters or centimeters).

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What is the smallest division on a measuring scale?

How many decimal places should you record for a measurement?

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Ruler B: 2.7 cm

Ruler A: 2.60 cm

1/10th of the smallest division on the ruler tells you the how many decimal places

Smallest division is the distance between closest marks Ruler A smallest division 1/10th cm Ruler B smallest division 1 cm

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How big is 1 cm compared to 1 meter?

How big is 1 mm

compared to 1 meter?

How big is 1 mm compared to 1 cm?

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1 cm is 1/100th of 1 m 100 cm = 1 m 1mm is 1/1000th of 1 m 1000 mm = 1 m

1 mm is 1/10th of 1 cm There are 10 mm in 1 cm 10 mm = 1 cm

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Accuracy of a measurement

Precision of a measurement

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Precision: How many decimal places you record for a measurement. Example: If your ruler has a smallest division of 1/10th cm, you can measure to 1/100th of a cm: 1.52 cm has a 1/100th place

Accuracy is how well an instrument matches a standard unit. Example: A meter stick should match a standard meter stick used by everyone. Heat or moisture can change an object representing a unit and be inaccurate.

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Is it possible to get an exact measurement?

Why or why not?

A student reports a measurement as 4.3 s ± 0.2 s

What does each number mean?

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The units of seconds (s) indicate that the student measured time. 4.3 s is the average time. ± 0.2 s is the average deviation, or precision, of this measurement. The true value is somewhere in the range 4.1 s to 4.5 s (4.3 – 0.2 = 4.1 and 4.3 + 0.2 = 4.5)

No. Each measurement is a range of values because of uncertainty or error . A measurement is not a single, exact number. Sources of error can be random errors and limited precision of the instrument. How you set up the experiment could also add errors. Example: Your experiment assumed that the table is flat, but it is not.

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What is the length at a, b, c, d – in cm?

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The smallest division on the ruler is 1/10th of a cm (each 1 cm is divided into 10 parts). You can estimate the hundredth place: a = 0.00 cm b = 1.50 cm c = 2.30 cm d = 3.20 cm

The smallest division on the ruler is 1/10th of a cm (each 1 cm is divided into 10 parts). You can estimate the hundredth place. Length of object = 2.35 cm

What is the length of the red object in cm?

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Record the volume of water in mL and cm3.

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The smallest division on the scale is 10 mL You can estimate the one’s place on the scale (1/10th of the smallest division). V = 48 mL = 48 cm3

(Note that 1mL = 1 cm3) – 1 mL is the same as 1 cm3.

Always start measuring at the 0 mark. The smallest division on the ruler is 1/10th of a cm (each 1 cm is divided into 10 parts). So, you can estimate the hundredth place. Length of object = 0.45 cm

Record the length of the red object in cm to correct precision.

mL

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Record the mass on this triple-beam balance in grams.

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M = 300 g + 30 g + 5 g = 335 g

Record the mass on this triple-beam balance in grams.

M = 0 g + 30 g + 7.3 g = 37.3 g

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A student measures a length of 2.6 cm.

What is the smallest division

on the ruler?

A student measures a length of 2.60 cm.

What is the smallest division

on the ruler?

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In a measurement, the last digit is estimated to the tenth place of the smallest division. So, the tenth place must be estimated (1/10th of 1), and the ruler marks are 1 cm apart.

In a measurement, the last digit is estimated as the tenth place of the smallest division. In this example, the hundredth place is estimated (1/10th of 0.1cm), and the ruler marks are 0.1 cm apart or 1 mm apart.

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100 cm = 1 m 89 cm = ? m

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1 cm is 1/100th of 1 m Divide or multiply by 100? A meter is a larger unit. This means there will be fewer m for the same number of cm → divide by 100 89 cm = 0.89 m

What is ½ of the smallest division

on each ruler in cm?

Smallest division is the distance between closest marks Ruler A: ½ of 0.1 cm = 0.05 cm Ruler B: ½ or 1 cm = 0.5 cm

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13.5 mm = ? cm

10.12 cm = ? mm

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There are 10 mm in 1 cm 1 cm is a bigger unit – there are fewer cm for the same number of mm Divide 13.5 by 10 1.35 cm

There are 10 mm in 1 cm 1 mm is a smaller unit – there are more mm for the same number of cm Multiply 10.12 by 10 → 100.12 mm

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Why is a repeating decimal impossible in science?

The bar over the “3” means that the 3 is “repeating” to infinity: This is impossible in science. No real-world value can be known to infinite precision (infinite digits). Instead, every measured value has uncertainty or error.

Why is it important to use the same standard unit system in a project?

The Metric (or SI) unit system uses meters and kilograms.

The British unit system uses inches and slugs. When working on a project, such as

constructing a house or the Mars Orbiter, or creating the software to run the Mars Orbiter, it is important to agree on the same unit system to avoid errors.

0.3 0.333333...cm cm=

0.3 0.333333...cm cm=

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Find the area in cm and in mm:

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In cm: A = L x W = (2.11 cm)(5.08 cm) = 10.72 cm2

In mm: First, convert cm to mm L = 5.08 cm = 50.8 mm W = 2.11 cm = 21.1 mm Then, find area: A = L x W = (50.8 mm)(21.1 mm) = 1072 mm2

W = 2.11 cm

L = 5.08 cm

Find the volume in cm and in mm:

L = 5.08 cm W = 2.11 cm

H = 3.98 cm

In cm: V = L x W x H = (2.11 cm)(5.08 cm)(3.98 cm) = 42.66 cm3

In mm: First, convert to mm L = 5.08 cm = 50.8 mm W = 2.11 cm = 21.1 mm H = 3.98 cm = 39.8 mm Then, find volume: V = L x W x H = (50.8 mm)(21.1 mm)(39.8 mm) = 4266 mm3

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What are the units of Area?

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Area is reporting in units of any length2. Example: cm2, m2, in2, ft2.

What are the units of Volume?

Volume is reporting in units of any length3. Example: cm3, m3, in3, ft3. Volume is also reported in units of fluid volume. Example: Liters (L), milliliters (mL)

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Density

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Density is the amount of mass in each unit of volume. Example: Gold density is 19.3 g/cm3. This means that there are 19 g in each 1 cm3. Example: Aluminum density is 2.7 g/mL. This means that there are 2.7 g in each 1 mL.

Find the density a 100 g rectangular prism with these dimension (lengths):

L = 5.08 cm W = 2.11 cm

H = 3.98 cm

Find volume: V = L x W x H = (2.11 cm)(5.08 cm)(3.98 cm) = 42.66 cm3

Find density:

MDV

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3 3

100 2.3442.66

M g gDV cm cm

= = =

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If materials are different, do they also have different density?

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Density is the amount of mass in each unit of volume. Density is different for different materials. Example: Gold density is 19.3 g/cm3. Aluminum density is 2.7 g/cm3. Gold has more mass in 1 cm3 than aluminum.

1 cm3 = ? mL

1 cm3 = 1 mL 1 cm3 is a unit of calculated volume, and 1 mL is a unit of liquid volume.

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How do you find volume of regular solids?

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Regular solids: Measure dimensions (e.g., length, radius) Calculate volume using a formula. Different shapes have different formulas.

How do you find volume

of irregular solids?

Use any liquid and a beaker or graduated cylinder: 1. Measure liquid volume without object 2. Measure liquid volume with object. Make

sure the object is fully under the liquid. 3. Subtract the two volumes to get the

volume of the object. Example:

V of object = 150 L – 50 L = 100 L

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How can you identify the material of an unknown pure substance?

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Density lets you identify a pure material because different materials have different densities. Example: You do an experiment to get the density of an unknown substance = 2.7 g/cm3. When you look up this density, it is for Aluminum.

T/F Less dense substances float on top of more dense substances.

True. Less dense substances float on top of more dense materials.

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Why do you make multiple measurements of the same quantity in lab?

(multiple trials)

What are random errors in an experiment?

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By making multiple measurements, you reduce or minimize random errors. You can calculate random error from multiple trials by finding the average deviation.

Random errors occur because you did not control all variables in your experiment. Some values will be too high, and some will be too low by random chance.

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How do you determine sources of error in the experiment?

Every variable you measure has experimental error. Ask: - What about my setup or measurement technique could have caused errors? - Are the assumptions I made about the experiment true? Example: Ramp length could have been off by ±0.5 cm because we did not consistently start the marble at the top of the ramp.

How do you calculate % error in a lab?

Suppose you want to find percent error between your value of gravitational acceleration on Earth of 11 m/s2 and the accepted value of 9.81 m/s2.

1) Subtract the two values: 11 - 9.81 = 1.19 2) Divide by the value you are comparing

your result to: 1.19/9.81 = 0.12

3) Multiply by 100 to present as %: 0.12 x 100 = 12%

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What are the key sections in a lab report?

1.Objective: Lab goal or question 2.Materials: List of materials you used 3.Procedure: Numbered steps for

a) setting up the experiment b) collecting data

4.Data: Labeled and organized measured data

5.Analysis: Calculations using measured data to answer a lab goal

6.Conclusion: Summarizes goal and results

How do you write a lab Conclusion?

1) Restate the lab Objective. Example: The purpose of this experiment was to measure the acceleration of gravity on Earth.

2) Summarize results. Example: Based on the analysis, the acceleration of gravity on Earth is 11 m/s2. This results differs from the accepted result of 9.81 m/s2 by 12%.

3) State possible sources of error.

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How do you calculate precision of data (or average deviation)

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1. Measure the same quantity multiple times. Example: 11s, 13s, 12s, 14s, and 12s

2. Average the values. Example: (11+13+12+14+12)/5=12.4 s

3. Subtract each value from the mean. Make all results positive!

4. Average the deviation values from step 3.

s

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What do these unit prefixes mean: milli- centi- kilo-

How many grams are in 10 kg?

1 kg = 1000 g So 10 kg = 10 x 1000 g = 10,000 g 1 g is a smaller unit. So, there will be more grams for the same amount in kg.

milli- is 1/1000th Example: 1 millimeter is 1/1000th of 1 m centi- is 1/100th Example: centimeter is 1/100th of 1 m kilo- is 1000 times Example: kilogram is 1000 grams

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Find the mass of a rectangular object with a density of 2.3 g/cm3:

L = 5.08 cm W = 2.11 cm

H = 3.98 cm

Find volume: V = L x W x H = (2.11 cm)(5.08 cm)(3.98 cm) = 42.66 cm3

Find the mass:

MDV

=

32.3 gM DV

cm= = 342.66 cm

( ) 98g=

MD VV

⋅ = V⋅

M DV=

Solve for mass

Find the volume of a 100 g rectangular object with a density of 2.3 g/cm3:

Find volume:

MDV

=

3

3

100 432.3

M gV cmgD

cm

= = =

MD VV

⋅ = V⋅ ( )

( )

V

DV M D

D

×

= ÷

VD

MD

MVD

=

=

Solve for volume

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