This document contains notes from a math lesson on converting rational numbers to decimals using long division. It includes examples of terminating and repeating decimals, exercises for students to practice long division conversions, and questions about determining whether decimals will terminate or repeat based on the remainders. The lesson emphasizes using rational number conversions and long division in problem solving contexts.
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.
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
Macroeconomics- Movie Location
This will be used as part of your Personal Professional Portfolio once graded.
Objective:
Prepare a presentation or a paper using research, basic comparative analysis, data organization and application of economic information. You will make an informed assessment of an economic climate outside of the United States to accomplish an entertainment industry objective.
How to Make a Field invisible in Odoo 17Celine George
It is possible to hide or invisible some fields in odoo. Commonly using “invisible” attribute in the field definition to invisible the fields. This slide will show how to make a field invisible in odoo 17.
Embracing GenAI - A Strategic ImperativePeter Windle
Artificial Intelligence (AI) technologies such as Generative AI, Image Generators and Large Language Models have had a dramatic impact on teaching, learning and assessment over the past 18 months. The most immediate threat AI posed was to Academic Integrity with Higher Education Institutes (HEIs) focusing their efforts on combating the use of GenAI in assessment. Guidelines were developed for staff and students, policies put in place too. Innovative educators have forged paths in the use of Generative AI for teaching, learning and assessments leading to pockets of transformation springing up across HEIs, often with little or no top-down guidance, support or direction.
This Gasta posits a strategic approach to integrating AI into HEIs to prepare staff, students and the curriculum for an evolving world and workplace. We will highlight the advantages of working with these technologies beyond the realm of teaching, learning and assessment by considering prompt engineering skills, industry impact, curriculum changes, and the need for staff upskilling. In contrast, not engaging strategically with Generative AI poses risks, including falling behind peers, missed opportunities and failing to ensure our graduates remain employable. The rapid evolution of AI technologies necessitates a proactive and strategic approach if we are to remain relevant.
The Roman Empire A Historical Colossus.pdfkaushalkr1407
The Roman Empire, a vast and enduring power, stands as one of history's most remarkable civilizations, leaving an indelible imprint on the world. It emerged from the Roman Republic, transitioning into an imperial powerhouse under the leadership of Augustus Caesar in 27 BCE. This transformation marked the beginning of an era defined by unprecedented territorial expansion, architectural marvels, and profound cultural influence.
The empire's roots lie in the city of Rome, founded, according to legend, by Romulus in 753 BCE. Over centuries, Rome evolved from a small settlement to a formidable republic, characterized by a complex political system with elected officials and checks on power. However, internal strife, class conflicts, and military ambitions paved the way for the end of the Republic. Julius Caesar’s dictatorship and subsequent assassination in 44 BCE created a power vacuum, leading to a civil war. Octavian, later Augustus, emerged victorious, heralding the Roman Empire’s birth.
Under Augustus, the empire experienced the Pax Romana, a 200-year period of relative peace and stability. Augustus reformed the military, established efficient administrative systems, and initiated grand construction projects. The empire's borders expanded, encompassing territories from Britain to Egypt and from Spain to the Euphrates. Roman legions, renowned for their discipline and engineering prowess, secured and maintained these vast territories, building roads, fortifications, and cities that facilitated control and integration.
The Roman Empire’s society was hierarchical, with a rigid class system. At the top were the patricians, wealthy elites who held significant political power. Below them were the plebeians, free citizens with limited political influence, and the vast numbers of slaves who formed the backbone of the economy. The family unit was central, governed by the paterfamilias, the male head who held absolute authority.
Culturally, the Romans were eclectic, absorbing and adapting elements from the civilizations they encountered, particularly the Greeks. Roman art, literature, and philosophy reflected this synthesis, creating a rich cultural tapestry. Latin, the Roman language, became the lingua franca of the Western world, influencing numerous modern languages.
Roman architecture and engineering achievements were monumental. They perfected the arch, vault, and dome, constructing enduring structures like the Colosseum, Pantheon, and aqueducts. These engineering marvels not only showcased Roman ingenuity but also served practical purposes, from public entertainment to water supply.
4. Module 2 Lesson 14.notebook
4
November 20, 2014
Problem Set Solutions
0.04
3.3125
S.69
5. Module 2 Lesson 14.notebook
5
November 20, 2014
Example 1: Can All Rational Numbers Be Written as Decimals?
a. Using the division button on your calculator, explore various quotients of integers 1 through 11.
Record your fraction representations and their corresponding decimal representations in the
space below.
b. What two types of decimals do you see?
S.70
6. Module 2 Lesson 14.notebook
6
November 20, 2014
Example 2: Decimal Representations of Rational Numbers
S.70
In the chart below, organize the fractions and their corresponding decimal representations listed in
example 1 according to their type of decimal.
Terminating Non-Terminating
What do these fractions have in common? What do these fractions have in common?
The denominators
are only divisible by
factors of 2's and
5's.
The denominators
are only divisible by
another factor other
than factors of 2's
and 5's.
7. Module 2 Lesson 14.notebook
7
November 20, 2014
Example 3: Converting Rational Numbers to Decimals Using Long-Division
Use the long division algorithm to find the decimal value of
S.71
8. Module 2 Lesson 14.notebook
8
November 20, 2014
Exercise 1:
Convert each rational number to its decimal form using long division
a.
b.
S.71
9. Module 2 Lesson 14.notebook
9
November 20, 2014
Example 4: Converting Rational Numbers to Decimals Using Long-Division
Use long division to find the decimal representation of
S.72
10. Module 2 Lesson 14.notebook
November 20, 2014
10
Question:
What part of your calculation causes the decimal to repeat?
11. Module 2 Lesson 14.notebook
November 20, 2014
11
Exercise 2
Calculate the decimal value of the fraction below using long division. Express your answers using
bars over the shortest sequence of repeating digits.
a. b.
c. d.
S.72
12. Module 2 Lesson 14.notebook
November 20, 2014
12
Exercise 2
Calculate the decimal value of the fraction below using long division. Express your answers using
bars over the shortest sequence of repeating digits.
a. b.
c. d.
S.72
13. Module 2 Lesson 14.notebook
November 20, 2014
13
Example 5: Fractions Represent Terminating or Repeating Decimals
How do we determine whether the decimal representation of a quotient of two integers, with the
divisor not equal to zero, will terminate or repeat?
If the remainder is zero:
If the remainder is not zero:
S.73
14. Module 2 Lesson 14.notebook
November 20, 2014
14
Example 6: Using Rational Number Conversions in Problem Solving
S.73
a. Eric and four of his friends are taking a trip across the New York State Thruway. They
decide to split the cost of tolls equally. If the total cost of tolls is $8, how much will each
person have to pay?
b. Just before leaving on the trip, two of Eric's friends have a family emergency and cannot
go. What is each person's share of the $8 toll now?
15. Module 2 Lesson 14.notebook
November 20, 2014
15
Closing:
1.) What should you do if the remainders
of a quotient of integers do not seem to
repeat?
2.) What is the form for writing a
repeating decimal?
