1. Indices, also known as exponents, are used to succinctly represent extremely large or small numbers. They allow writing numbers like 1.44 x 108 km instead of 144,000,000 km.
2. Standard form is a notation where a number is written as A x 10n, where 1 ≤ A < 10 and n is an integer. This puts all numbers in a normalized form and makes them easier to comprehend.
3. Laws of indices allow mathematical operations like multiplication and division to be performed on expressions with common bases or exponents.
Algebra is used in many field in many different ways to solve equation problems, and in business algebra is also used or in our day to day life it is also used. ... Algebra is a way of keeping track of unknown values, which can be used in equations.
Algebra is used in many field in many different ways to solve equation problems, and in business algebra is also used or in our day to day life it is also used. ... Algebra is a way of keeping track of unknown values, which can be used in equations.
A Novel Methodology for Designing Linear Phase IIR FiltersIDES Editor
This paper presents a novel technique for
designing an Infinite Impulse Response (IIR) Filter with
Linear Phase Response. The design of IIR filter is always a
challenging task due to the reason that a Linear Phase
Response is not realizable in this kind. The conventional
techniques involve large number of samples and higher
order filter for better approximation resulting in complex
hardware for implementing the same. In addition, an
extensive computational resource for obtaining the inverse
of huge matrices is required. However, we propose a
technique, which uses the frequency domain sampling along
with the linear programming concept to achieve a filter
design, which gives a best approximation for the linear
phase response. The proposed method can give the closest
response with less number of samples (only 10) and is
computationally simple. We have presented the filter design
along with its formulation and solving methodology.
Numerical results are used to substantiate the efficiency of
the proposed method.
A guide to Tensor and its applications in Machine Learning.pdfVanessa Bridge
Analysis of applications of tensor based algorithms to improve performance of many machine learning algorithms for training, detection and classification.
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Bills have a main role in point of sale procedure. It will help to track sales, handling payments and giving receipts to customers. Bill splitting also has an important role in POS. For example, If some friends come together for dinner and if they want to divide the bill then it is possible by POS bill splitting. This slide will show how to split bills in odoo 17 POS.
Operation “Blue Star” is the only event in the history of Independent India where the state went into war with its own people. Even after about 40 years it is not clear if it was culmination of states anger over people of the region, a political game of power or start of dictatorial chapter in the democratic setup.
The people of Punjab felt alienated from main stream due to denial of their just demands during a long democratic struggle since independence. As it happen all over the word, it led to militant struggle with great loss of lives of military, police and civilian personnel. Killing of Indira Gandhi and massacre of innocent Sikhs in Delhi and other India cities was also associated with this movement.
Read| The latest issue of The Challenger is here! We are thrilled to announce that our school paper has qualified for the NATIONAL SCHOOLS PRESS CONFERENCE (NSPC) 2024. Thank you for your unwavering support and trust. Dive into the stories that made us stand out!
The French Revolution, which began in 1789, was a period of radical social and political upheaval in France. It marked the decline of absolute monarchies, the rise of secular and democratic republics, and the eventual rise of Napoleon Bonaparte. This revolutionary period is crucial in understanding the transition from feudalism to modernity in Europe.
For more information, visit-www.vavaclasses.com
Ethnobotany and Ethnopharmacology:
Ethnobotany in herbal drug evaluation,
Impact of Ethnobotany in traditional medicine,
New development in herbals,
Bio-prospecting tools for drug discovery,
Role of Ethnopharmacology in drug evaluation,
Reverse Pharmacology.
2024.06.01 Introducing a competency framework for languag learning materials ...Sandy Millin
http://sandymillin.wordpress.com/iateflwebinar2024
Published classroom materials form the basis of syllabuses, drive teacher professional development, and have a potentially huge influence on learners, teachers and education systems. All teachers also create their own materials, whether a few sentences on a blackboard, a highly-structured fully-realised online course, or anything in between. Despite this, the knowledge and skills needed to create effective language learning materials are rarely part of teacher training, and are mostly learnt by trial and error.
Knowledge and skills frameworks, generally called competency frameworks, for ELT teachers, trainers and managers have existed for a few years now. However, until I created one for my MA dissertation, there wasn’t one drawing together what we need to know and do to be able to effectively produce language learning materials.
This webinar will introduce you to my framework, highlighting the key competencies I identified from my research. It will also show how anybody involved in language teaching (any language, not just English!), teacher training, managing schools or developing language learning materials can benefit from using the framework.
We all have good and bad thoughts from time to time and situation to situation. We are bombarded daily with spiraling thoughts(both negative and positive) creating all-consuming feel , making us difficult to manage with associated suffering. Good thoughts are like our Mob Signal (Positive thought) amidst noise(negative thought) in the atmosphere. Negative thoughts like noise outweigh positive thoughts. These thoughts often create unwanted confusion, trouble, stress and frustration in our mind as well as chaos in our physical world. Negative thoughts are also known as “distorted thinking”.
1. Slide 1
01
Chapter
Indices and Standard Form
Earth to Sun: 144 000 000 km
Earth to Moon: 384 835 km
What about the distance from the Earth to the Moon?
We know that the Sun is very far from the Earth.
But how far exactly is it?
How many digits are needed to represent this distance?
It’s 144 000 000 km,
or 1.440 00 x 100 000 000 km,
or 1.440 00 x 108 km.
2. Slide 2
01
Chapter
Indices and Standard Form
Earth:
6.6 x 1021 metric tons Sun:
22 x 1027 metric tons
Moon:
7.3 x 1019 metric tons
Besides the distances mentioned earlier, even the masses of the
Earth, the Moon and the Sun are pretty large too.
The numbers involved are so large that we make use of
INDICES to represent them.
3. Slide 3
01
Chapter
Indices and Standard Form
Besides representing very large numbers, we can also make
use of INDICES to represent very small numbers.
Some examples: diameter of a strand of hair, size of
an atom, size of a bacterium
Diameter of a human hair: 0.000 025 4 m
We can rewrite it as
25.4 x 0.000 001 m,
or 25.4 x 10-6 m
What are INDICES then?
4. Slide 4
01
Chapter
Indices and Standard Form
1.440 00 x 108 km 25.4 x 10-6 m
These numbers are called INDICES.
We make use of INDICES to represent extremely
LARGE or small numbers.
INDICES saves us from writing long string of
digits, saving time and effort, and reducing the
chance of missing out digits.
5. Slide 5
01
Chapter
Indices and Standard Form
Imagine having to write out 22 x 1027 which is the
value of the mass of the Sun, in full in your
assignment about the Solar System.
22 x 10 27
= 22 000 000 000 000 000 000 000 000
6. Slide 6
01
Chapter
Indices and Standard Form
2 x 2 x 2 can be written as 23,
where
23 Index / Exponent
Base
7. Slide 7
01
Chapter
Indices and Standard Form
am3
5 = a xx aa x xa a … x a
x a a
m times
8. Slide 8
01
Chapter
Indices and Standard Form
Below are the laws of indices for expressions with a common
base.
a xa = a
m n m+n
a a =a
m n m-n
(a ) = a
m n m n
9. Slide 9
01
Chapter
Indices and Standard Form
Summary
a xa = a
m n m+n
a a =a
m n m–n
(a ) = a = a
m n m n mn
10. Slide 10
01
Chapter
Indices and Standard Form
Below are the laws of indices for expressions with a common
index.
a3 b3
x
= (a (a) (a) x b) (b) (b)
(a) (a (a (b) b) b)
=
3
= (a b)
11. Slide 11
01
Chapter
Indices and Standard Form
a 3 (a) (a) (a)
a a
3
=
b (b) (b) (b)
b b
3
a a a
=
b b b
12. Slide 12
01
Chapter
Indices and Standard Form
Summary
a x b = (ab)
m m m
a m
a b = ( b)
m m
13. Slide 13
01
Chapter
Indices and Standard Form
a = 1
0 Zero Index
- =
-3 1
a
2 n
8 n
3
Negative Index
a
2
12 n
3
2
8
4
a = √a
3
n
√8
√4
2 Fractional Index
14. Slide 14
01
Chapter
Indices and Standard Form
More on Fractional Index
13 n
3
8
a n
= √a
√8
2
m
1n n m
a = √a
2
13 3 2
8 = √4
64
8
15. Slide 15
01
Chapter
Indices and Standard Form
Summary
a =1
0
1
a = an
-n
1 n m n
a n = √a a n = √am
16. Slide 16
01
Chapter
Indices and Standard Form
Equations Involving Indices
4 x = 16
4 2
x = 2
17. Slide 17
01
Chapter
Indices and Standard Form
Index
Earth to Sun: (plural: indices)
8
1.440 00 x 10 km
Then what is this form of
expressing numbers known as?
1.440 00 x 108 — standard form of
144 000 000
A, where 1 ≤ A < 10 nn is an integer.
In general, A x 10
18. Slide 18
01
Chapter
Indices and Standard Form
Standard form for very large numbers
144 000 000
8 6 3 Numbers larger than 1,
move to the left
Is 1 ≤ A < 10 now?
Yes! So, in standard form:
1.440 00 x 108
19. Slide 19
01
Chapter
Indices and Standard Form
Standard form for very small numbers
Numbers smaller than 1,
move to the right.
0.000 000 144
3 6 7
Is 1 ≤ A < 10 now?
Yes! So, in standard form:
-7
1.440 00 x 10