Tredyffrin/Easttown School District



X Unit 2 Notes – Measurement

A. Purpose & History of Measurement

a. Why Measure?

i. Measurements were created to accomplish many task including:

1.

2.

3.

b. What can be Measured?

i. There are many physical properties that can be measured in the world around us.

ii. Any property that can be measured and assigned a numerical value is said to be a ______________________ property (think quantity).

1. Examples of quantitative properties:

c. Systems of Measurement

i. There are two major systems of measurement in use today:

1. the Imperial (standard) units

2. the _______________ system

d. History of Measurement

i. Length was measured using the __________.

1. Cubit = the length of the forearm from the tip of the elbow to the tip of the middle finger

a. The cubit was divided into two spans, six hands, or 24 digits.

ii. The ________, __________, and _________ were derived from these units.

1. The Roman foot was divided into 12 __________ and 16 ________. The Roman mile consisted of ____________ feet (or 1000 paces).

2. ________________________________ changed the mile to 5,280 feet (what we know it as today)

e. The Metric System & The Need for Standardization

i. During the development of measurements, the same unit came to measure slightly different amounts depending upon:

1.

2.

3.

ii. The _________________________ (often abbreviated as the SI system) is the measurement system preferred by scientists around the world.

1. Created by the ____________

2. Used by all but three nations worldwide (Burma, Liberia, and the _________)

iii. The metric system addresses the seemingly arbitrary relationship between different units for measuring the same property.

1. Ex. Why are there 12 inches in a foot but 3 feet in a yard?

iv. The metric system is based on powers of ______ which makes it easy to go from small units to large units within the base (____________, __________, ______________, etc.)

B. Taking Measurements

a. We often use the terms ________________ and __________________ to mean the same thing, when in actuality, they have different meanings.

i. In lab it is important to be both _________________ AND __________________.

b. Accuracy – refers to _____________________________________________________________ ______________________________________________________________________________

ACCURATE ONLY

i. Example: If you used a tape measure to measure a 100 yard football field, a measurement of 99.3 yards would be considered accurate.

c. Percent Error determines how accurate you are.

i. Equation:

ii. Ex.) A student reports the density of a pure substance to be 2.83 g/mL. The accepted value is 2.70 g/mL. What is the percent error for the student’s results?

d. Precision – refers to the ________________________ of measurements (how close measurements are to __________________________.

PRECISE ONLY ACCURATE & PRECISE

e. In lab, you will have to make many measurements using a number of different tools. Each tool should be read to the proper precision in order to be successful in lab.

i. In general, measurements should be made to have ______________________________ ____________________ than the smallest increment on the measuring device.

f. Determining Increments on Measuring Devices

i. Step #1: Subtract two adjacent numbered markings from each other

ii. Step #2: Count the number of marks, or increments, between numbered marks (including the top mark).

iii. Step #3: Divide the amount measured between numbered marks by the number of increments between numbered marks (Divide the number from Step #1 by the number from Step #2).

g. Certain vs. Uncertain Digits

i. The smallest increment on a measuring device is known as the ____________________.

1. This is because there is no estimating involved in determining that number; it is just read from the device.

ii. The _____________________________ is also called the __________________ digit.

1. All measurement must end with _______ and only ______ estimated digit!!!

iii. Examples:

What measurements are represented by the following letters?

A – D –

B – E –

C – F –

C. Significant Figures (a.k.a. Sig. Figs.)

a. Significant figures – all the digits in a measurement that are known with certainty plus _______ ______________________________________________________________________________

i. For the purposes of significant figures, there are two major categories:

1. Nonzero digits:

2. Zero digits:

b. Rules for Counting Sig Figs

i. All _________________________ are significant!

1. Ex.) 3269 ( ______ significant figures

257 ( ______ significant figures

1.234567 ( ______ significant figures

ii. Zeroes take three forms:

1. ________________ zeroes

2. ________________ zeroes

3. ________________ zeroes

iii. Leading Zeroes = zeroes that come ____________ the nonzero digits in a number.

1. Leading zeroes are placeholders only and are _____________ considered significant.

2. Ex.)

iv. Trapped Zeroes = zeroes ________________ two nonzero digits.

1. Trapped zeroes are _______________________________________.

2. Ex.)

v. Trailing Zeroes = zeroes that ______________ nonzero digits.

1. Trailing zeroes are only significant if there is a ____________________________ in the number.

2. Ex.)

vi. Exact Numbers: Any number which represents a numerical count or is an exact definition has an infinite number of sig figs and is NOT counted in the calculations.

1. Ex.)

vii. Practice: How many significant digits are in each of the following?

1. 1.034 s 4. 3000 m

2. 0.0067 g 5. 72 people

3. 12 apples

c. Rules for Using Sig Figs with Addition/Subtraction

i. Step #1: Determine the number of _________________________________ in each number to be added or subtracted.

ii. Step #2: Calculate the answer and then round the final number to the least number of _______________________________________ from Step #1.

iii. Examples:

d. Rules for Using Sig Figs with Multiplication/Division

i. Step #1: Determine the number of ____________________ in each number to be multiplied or divided.

ii. Step #2: Calculate the answer and then round the final number to the least number of ______________________________ from Step #1.

iii. Examples:

e. Practice with Significant Figures: Perform the following calculations and report your answer with the correct number of digits.

i. 23.456 ( 4.20 ( 0.010 =

ii. 0.001 + 1.1 + 0.350 =

iii. 17 ÷ 22.73 =

D. Scientific Notation

a. Scientific notation – a system for representing a number as a number between ____ and _____ multiplied by a _________________________.

i. Scientific notation is most useful for presenting very __________ or very ____________ numbers in a form that is easier to use.

1. Examples: 253,000,000,000,000,000,000 =

0.0000000000000000000253 =

b. In scientific notation, numbers are expressed as a number between 1 and 10 multiplied by 10 raised to an ______________________.

120.3 =

100 is the same as 102 so…

120.3 =

***Any easy way to determine the exponent of ten is to count the decimal positions that you move***

0.000001203 =

(The decimal has moved ____________________ ______ positions.)

1203000000 =

(The decimal has moved ________________ ______ positions.)

c. Practice: Convert between scientific notation and standard numerical notation.

i. 74,390,000 =

ii. 0.000009998 =

iii. -0.0000623 =

iv. 5.466 × 106 =

v. 2.3× 10-4 =

E. The Metric System

a. The metric system is based on a __________________ that corresponds to a certain kind of measurement.

i. Length =

ii. Volume =

iii. Weight (mass) =

b. Prefixes plus base units make up the metric system. (centi + meter = centimeter)

i. The three prefixes that we will use the most are _________, __________and ________.

|kilo |hecto |deca | Base Units |deci |centi |milli |

| | | |meter | | | |

| | | |gram | | | |

| | | |liter | | | |

ii. These prefixes are based on powers of 10 meaning every “step” is either ten times larger or ten times smaller.

1. Centimeters are ______________________________ than millimeters.

2. 1 centimeter =

a. Centimeters are 10 times larger than millimeters so it takes _________ millimeters for the same length.

3. Let’s move from a base unit to centi:

1 liter =

2 grams =

c. An easy way to move within the metric system is by moving the decimal point one place for each “step” desired.

i. Example: Change meters to centimeters.

1.00 meter =

ii. Example: Change meters to kilometers.

16093 meters =

***For every “step” from the base unit to kilo we moved the decimal 1 place to the left (the same direction as in the diagram above).

***If you move to the left in the diagram, move the decimal to the left. If you move to the right in the diagram, move the decimal to the right.

d. Practice: Convert from the original unit to the desired unit.

i. 400,000 cm = ??? kilometers

ii. 4,000 m = ??? kilometers

iii. 4,000 cm = ??? km

iv. 5 meters = ??? cm

v. 0.3 km = ??? m

vi. 4 km = ??? mm

F. Dimensional Analysis: Conversions Made Easy

a. Why convert?

i. When working with numbers from a system that is not familiar to you, being able to place them into a system you are familiar with will help you understand their significance.

b. Often times the relationship between two systems is expressed as a fraction we call a _____________________________________.

i. These take the form of an expression consisting of ______________________________ expressed in ____________________________________.

ii. Example of a conversion factor:

c. Since the values in the denominator and the numerator represent the same thing, the conversion factor is a fraction that equals ______ (even though it doesn’t look like it at first).

i. Since you are essentially multiplying by 1, you end up with a value that is equal to the value of the original number!

d. Practice: While flying solo across the country, a Boeing 767 cruises at an altitude of 33,000 feet. If there are 5,280 feet in a mile, how many miles above the ground is a 767 flying?

i. The key to properly setting up and solving the problem lies with the units. The units tell us how to set up & plug in the conversion factor!!

1. The goal when setting up the conversion factor is to get the units of the measurement given to us in the problem to cancel out, leaving only the units that we desire our answer to be expressed in.

ii. The Set-Up & Solving:

***You must set up the conversion factor so that the units cancel out***

e. Things to Consider

i. Since all conversion factors are represented by different numbers whose values are the same, we are never changing the value of our given number when we use conversion factors.

ii. In order to ensure the proper use of conversion factors, place the value with the units that we desire in our answer on the top of the fraction and the given units on the bottom.

f. Practice! Convert the following.

i. 16,280 inches to miles

ii. 1.5 years to seconds

................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download