Science 10th grade
LEARNING UNIT
WHERE ARE WE LOCATED
IN TIME AND SPACE?
LEARNING OBJECT
What is the relationship between our numeric
system and the scientific notation?
S/K
SKILL 1: Establish a relationship between the number
of significant figures and the uncertainty of an
experimental value.
SKILL 2: Differentiate between fundamental units and
derived units.
SKILL 3: Use unit conversion factors.
SKILL 4: Explain the differences between precision
and accuracy
SKILL 5: Use accuracy and precision parameters to
analyze two or more experimental data sets.
SKILL 6: Analyze and compare binary, decimal, and
vigesimal (used by the Mayan) systems
Language
Socio cultural context of
the LO
Curricular axis
Standard competencies
Background Knowledge
English Review topic
Vocabulary box
English
Colombia
Physical Environment
Use of biological, physical, and chemical models to
explain energy transformation and conservation.
The students must know the basics of conversion
factors, scientific notation, precision, accuracy,
uncertainty, numeric systems and significant figures.
Possessives and passive voice
Approximation: Mathematics, Physics. a result that
is not necessarily exact, but is within the limits of
accuracy required for a given purpose.
Figure: 1. Numerical symbol, especially an Arabic
numeral. 2. an amount or value expressed in
numbers. 3.figures, the use of numbers in calculating.
Measure: 1. a unit or standard of measurement. 2. a
system of measurement: liquid measure. 3.
instrument, as a graduated rod or a container of
standard capacity, for measuring.
NAME: _________________________________________________
GRADE: ________________________________________________
Introduction
Numbers have allowed us to quantify a great amount of things in the
world and in part of the universe. They have opened the way to
scientific, economic, and social advancements, and have helped us to
make calculations on shapes, distances, and measurements, as well as
to diagnose and perform other activities in which we use numbers.
There are several forms to express the number 1. It may represent both
large or small things, and there are several ways to write it. For
example, 1 apple = 1.0x100 apples or 1.0x101 mm = 1 cm= 1.0 x 10-1
dm. These are representations of the same measurement, but written
differently depending on the conversion system used.
With numbers, we can determine how accurate and precise a bowman, a
basketball player, a dice roller, or an analyst is, among a lot more things.
Remember that...
there are various numeric systems such as decimal (0 to 9), binary (0
and 1) and vigesimal, which is based on the number 20, among others.
Objectives
To discuss The importance of the International System of Units to in the
solution of problems.
Actively listen to classmates and recognize different points of view.
To explain the difference between accuracy and precision.
Presentation
Next, you will find a series of activities that will allow you to widen your
number skills. Numbers can be used for different purposes, and given
that their units can be converted for an easier, more practical, and
simpler usage, they allow us to work in different sciences and everydaylife situations.
Activity 1
Skill 1: Establish a relationship between the number of significant
figures and the uncertainty of an experimental value.
Significant figures are the smallest number of digits necessary to write a
given value in scientific notation without accuracy loss; figures allow us
to write really large or small figures, facilitating figure handling.
All measurement instruments use a device to express uncertainty, such
as ±. For example, if we have a scale that has 0.001 (three decimals)
and they vary one by one, you could say its uncertainty is ±0.001.
Significant figures are those that add truthful, not ambiguous,
information of certain experimental measure. These figures are
determined by their error margin (uncertainty), being those figures the
ones that occupy an equal to or a higher position than the order or
position of the error margin.
According to the above, the following rules apply:
1. Any figure different from zero showing an equal or higher amount
than the experimental uncertainty is significant (2.14153. ± 0.001) mm.
Therefore, in the previous example, 4 significant figures can be
observed, in addition to two more figures which are not significant as
they are higher than uncertainty.
2. When counting the number of figures, zeros to the left of the first
non-null figure are dismissed. For example: -(3.141592…±0.0001)
having 5 significant figures; or (0.041592…± 0.0001) having 3
significant figures.
3. All zeros between significant digits are significant.
Number
1.022
603
Significant figures
amount
4
3
4. The zeros to the left of the first non-null digit only indicate decimal
position. Ex. 0.0056 with 2 significant figures or 0.00001 with one
significant figure.
5. To write numbers higher than 1, zeros to the right of the point are
significant. Ex. 2.00 has three significant figures, or 0.00.020 has two
significant figures.
The following video will allow you to expand your knowledge on the
subject.
https://youtu.be/Gn97hpEkTiM
Learning Activity 1
In the following chart, match the figures to the corresponding
uncertainties.
Figures
1.3
0.00.00414
3.045
3.1416
50.45
3,383222
Uncertainties
±0.0001
±0.00001
±0.1
±0,001
±0,01
±0,001
Activity 2
SKILL 2: Differentiate fundamental units from derived units.
SKILL 3: Use conversion factors.
Conversion factors are the ones that allow us to work and change units
depending on the activity we are performing.
For example, if 1 m3 of water needs to be converted to 1 cm3:
Observe the starting unit (m3) and the one you want to obtain (cm 3).
Review the steps you need to go through to be certain that the result is
correct.
Now, let’s study a conversion example followed by a step-by-step
explanation on how said conversion was performed.
Taken from YouTube on May 12 – 16
www.youtube.com/watch?v=JEr-oqaS5d0
Learning Activity 2
1. Considering the following chart, solve the exercises: convert from m
to cm, from Kg to gr, m3 to ml and indicate which are fundamental and
derived.
2. Based on the chart International System of Units (SI), match on the
next table, the groups of derived units to their physical magnitude. Notice that
some of the derived units do not have only one fundamental unit.
a) Derived Units: square meter (m2), newton (N), volt (V), cubic meter
(m3), meter per second (m/s), Hertz (Hz).
b) Fundamental Units: ampere (A), meter (m), kilogram (kg), second (s).
c) Physical magnitudes: time, strength, surface, volume, frequency,
speed, length, mass, electric current.
Activity 3
Skill 4: Explain the differences between precision and accuracy
SKILL 5: Use precision and accuracy parameters to analyze two or more
experimental data sets.
In the following image the different ways in which you can give accuracy
and precision, followed by a video in which the image is explained.
Video Retrieved from YouTube on May 12 – 16
www.youtube.com/watch?v=8Cl5CeiT7hU
Four basketball players practice throwing the ball to the basketball rim.
Depending on the area the ball touches, they will get the following
score.
Score
Area
100
Score
50
Small frame
20
Big frame
10
Board edge
At the end, they obtained the following results:
P1
P2
P3
P4
Sh1
100
50
20
10
Sh2
100
50
20
20
Sh3
100
50
20
0
P1 precise and accurate, P2 accurate, but not precise given that
hit the small frame area, P3 the most precise, but not accurate
because the ball always hit the same big frame spot, and P4 the least
precise and accurate given that the ball did not hit the same spot nor
close the basketball rim.
Learn Activity
Four analysts, each of them performing the same Acid-Base Titration
with hydrochloric acid 1molar and sodium hydroxide 1molar, and 10.0ml
of acid are taken. Knowing that these two possess a 1 to 1 relationship,
their precise and accurate point is 10.0ml on sodium hydroxide by 10ml
of hydrochloric acid.
1st analyst hydroxide
ml
9.5
9.4
9.5
9.4
9.4
9.5
9.4
9.5
2nd analyst hydroxide
ml
10.2
10.1
10.2
9.8
9.9
9.9
9.8
10.1
3rd analyst hydroxide
ml
8.5
9.0
10.7
8.2
8.3
11.0
9.2
10.4
9.5
10.2
8.5
1. Solve the problem above following the step-by-step showed in the
following video. Retrieved from QG, I. y. (March 8, 2016). :
https://www.youtube.com/watch?v=HGf5bN7K4u8
2. Graph each of the data sets in their respective Cartesian plane where
the X-axis is acid ml and the Y-axis hydroxide ml.
3. Explain the differences between precision and accuracy
Activity 4
Skill 6: Analyze and compare the binary, decimal and vigesimal (used
by the Mayan’s) systems
Vigesimal system
The Mayan vigesimal system it is written from bottom to top
It’s a system where the numerals are formed by three symbols:
•
•
•
The period equals a unit.
The horizontal line, which is equivalent to five.
The shell, which is zero.
With these symbols the Mayans created a vigesimal numeration system
(meaning (meaning 20 by 20), that allowed to have a positional value,
giving the possibility to write and do great mathematical and
astronomical calculations.
To write a number bigger than twenty its value change, depending on
the position the symbols are in, given tan their writing it’s laid vertically,
from bottom to top:
1. On the first order (the bottom), units from 0 to 19 are written.
2. On the second level 20-element group are represented, meaning
each symbol has an equivalent value to multiply by 20 its own
value (20 x 1).
3. On the third level, each symbol has an equivalent value to multiply
by 400 its own value (20 x 20 x 1).
4. On the fourth level, a period will be equivalent to 20 x 20 x 20 x 1,
meaning 8.000.
This numeration system is additive, because the symbols’ value are
added to know a number. The line will not be repeated more than four
times.
If 5 lines are needed, then a line substitutes them.
The line does not appear more than 3 times. If 4 lines are needed, then
the number is equal or higher than 20.
It should be noted, however that the Mayan numeration system
presents an irregularity when used to indicate dates.
In this case, the symbols written on the third level are equal to
18×20×1; this means each period equals 360 units and the line,
therefore would equal 360 x 5=1.800.
This irregularity has to do with the fact that the Mayan years are formed
by 360 days, the closest 20 multiple to 365.
In summary, for the date calculation the period on the third level
represents 360 and for all other 400.
Taken from (LEXIS, 2016) ; (Lapolillacubana’s Weblog, 2016)
Binary System
The binary system, in mathematics and computing, is a numeration
system in which the number are represented using only zeros and ones
(0 and 1).
Computers work internally with two voltage levels, so their natural
numeration system is binary (on = 1, off = 0).
The decimal system
The decimal system is a positional numeration system in which amounts
are represented using powers of 10 as an arithmetical base. The group
of symbols used it’s integrated by 10 different figures: 0, 1, 2, 3, 4, 5,
6, 7, 8 y 9.
Learning Activity
Observe the following chart, establish comparisons, analyze and find
differences and similarities.
Summary
According to all seen previously we can say there are several types of
numeric systems that are binary, decimal, and vigesimal, with
differences and similarities in writing and structure.
The International System of Units, that has as foundation to do different
types of conversions (from a fundamental unit to a derived or vice
versa), used in different areas, scientific being one of them; in it the
trials performed by analysts or students will require accuracy and
precision, and the accuracy is understood as the proximity to the
theoretical value and precision as the repeatability being this the
capability to perform several times the same trial always obtaining
similar results.
Working with high accuracy instruments or not, we must observe how
many uncertainty figures does it have to be able to analyze data, having
the exact amount of significant figures, and depending on the amount of
number that the figure has it can be expressed in scientific notation.
Homework
The following activities will allow you to reinforce your knowledge.
1. In groups of 5 people, build a polygon and practice shots with a ball,
as in the example of the basketball players above. From the results,
identify who was the most precise, and who was the most accurate.
Support your answer.
2. Review why Uncertainty and Significant figures may vary.
3. Review what fundamental and derived units are.
4. Give examples of situations in which the following numeric systems
can be used: decimal, vigesimal, and binary. Support your answer.
5. Convert the following measures and answer if the International
System of Units is important for physics and everyday life. Support your
answer.
Evaluation
1. Match column A to definitions in column B.
Column A
Column B
1. ___ Significative figure
a. Mathematic formula
2. ___ Fundamental figures
b. Points in a same area.
3. ___ Precision
c. Smallest number of digits
4. ___ Mayan vigesimal system
d. Change units.
5. ___ Derived
e. From bottom to top.
6. ___ Conversion factors
f. Real measurement standard
2. Choose true (T) or false (F) accordingly:
a) The Mayan vigesimal numeration system is additive ( )
b) In the binary system, numbers are represented using zero, one,
and two ( )
c) Uncertainty applies only to some measurement instruments ( )
3. Multiple choice questions with single answer; mark with an x the
letter corresponding to the right answer:
A million (1,000,000) is equivalent to:
a) 1 x 106
b) 1 x 10-6
c) 10 x 106
d) 10 x 10-6
Two thousand five hundred and forty mL (2,540 mL) equals:
a) 254 L
b) 2.54 L
c) 25.40 L
d) 2.5 L
12.5 mL equals:
a) 12.5 m³
b) 12.5 x 10 -5 m³
c) 1.25 m³
d) 1.25 x 10 -5 m³
4. Represent the following numbers from the Mayan vigesimal system in the
decimal system:
Answer: _____
Answer: _____
Answer: _____
Bibliography
International System of Units, Retrieved from:
https://empoweryourknowledgeandhappytrivia.files.wordpress.com/2015/03/in
ternational-system-of-units.jpg
International System. Retrieved from:
http://www.houghtonmifflinbooks.com/booksellers/press_release/studentscien
ce/quiz/15a.shtml
LEXIS. (05/03/2016). LEXIS . Retrieved from: LEXIS:
https://sendafonaments.wordpress.com/2009/09/04/el-sistema-denumeracion-maya-numeros-mayores-de-100/
Measurement Conversion, Retrieved from: https://s-media-cacheak0.pinimg.com/736x/30/4b/3a/304b3a1cf32862a973a2a296feb4ebe1.jpg
METROLOGIA Y NORMALIZACIÓN. (12/04/2016), Retrieved from:
http://gfmetrologia.mex.tl/:http://gfmetrologia.mex.tl/imagesnew2/0/0/0/2/0/
2/8/8/5/1/diagrama derivadas.jpg
QG, I. y. (08/03/2016). www.youtube.com. Retrieved from:
https://www.youtube.com/watch?v=HGf5bN7K4u8
The Decimal System. Retrieved from:http://04.educdn.com/files/static/learningexpressllc/9781576856215/WHAT_S_A_DECIMAL_
03.GIF
Glossary
Accuracy: It refers to how close is a measured value to its real value.
Conversion Factors: They allow making different changes between
fundamental and derived units or vice versa.
Derived Units: Unit obtained mathematically from basic units.
Fundamental or Basic Units: Are the ones with a real measurement
standard, being 7: "meter (m), length unit, kilogram (kg), mass unit, second
(s), time unit, ampere (A), electric current unit, kelvin (K), temperature unit,
mole (mole), amount of a substance, candela (cd), luminous intensity unit"
Precision: It refers to the dispersion of the set of values obtained from
repeated magnitude measurements.
Quantify: Express a magnitude through numbers.
Scientific Notation: “also called pattern or exponential notation”, is a way to
write numbers in an easier way when they are too large (100000000000) or
small (0.00000000001). The use of notation is based on powers of ten (the
cases exemplified before in scientific notation, would be 1 × 10 11 and 1 ×
10−11, respectively"
Significant Figure: “They represent the use of one or more uncertainty scales
in certain approximations. For instance, it is said that 4.7 has 2 significant
figures, while 4.70 has 3"