Rational and irrational numbers by Kashae Alexander
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To multiply rational numbers, convert them to decimals and multiply the decimals. Rational numbers are fractions with a numerator and denominator, while irrational numbers go on indefinitely as decimals and cannot be expressed as fractions. When multiplying a rational number and an irrational number, the result will always be irrational, as it is not possible to express an irrational number as a fraction.
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Even numbers are numbers that can be divided evenly by 2 and end in 0, 2, 4, 6, or 8, while odd numbers cannot be divided evenly by 2 and end in 1, 3, 5, 7, or 9. The rules for adding, subtracting and multiplying even and odd numbers always result in a whole number that is either even or odd, but dividing numbers can result in a fraction which is neither even nor odd.
Even and odd numbers
Even numbers are numbers that can be divided evenly by 2 and end in 0, 2, 4, 6, or 8, while odd numbers cannot be divided evenly by 2 and end in 1, 3, 5, 7, or 9. The rules for adding, subtracting and multiplying even and odd numbers always result in a whole number that is either even or odd, but dividing numbers can result in a fraction which is neither even nor odd.
DIGITAL TEXTBOOK
This document discusses irrational numbers and rounding numbers to a certain number of decimal places. It begins by explaining that some numbers like pi or the square root of 2 cannot be written as a fraction of two integers, and are therefore considered irrational. It then provides examples of irrational numbers and explains how to identify them. The document concludes by demonstrating how to round numbers, both rational and irrational, to a specified number of decimal places through examples such as rounding pi to 4 decimal places.
1-Introduction-to-Maths.pdf
This math module covers basic arithmetic concepts such as rounding, order of operations, and mental computation strategies. It includes 1) an introduction to arithmetic focusing on integers, operations, and place value; 2) refreshing skills like addition, subtraction, multiplication, and division of whole numbers; and 3) working with decimals, rounding, and estimating. The document provides examples and practice problems to help explain and apply these fundamental math topics.
Number systems
This document provides an overview of different number systems:
1. It defines six types of numbers: natural numbers, whole numbers, integers, rational numbers, irrational numbers, and real numbers.
2. Natural numbers are used for counting and start at 1. Whole numbers are natural numbers with 0 included. Integers include whole numbers and their negatives.
3. Rational numbers can be written as fractions with integer numerators and denominators. Irrational numbers cannot be written as fractions with integers and have non-repeating decimals.
4. Real numbers include all rational and irrational numbers.
PPT1_Rational-and-Irrational-Numbers-PowerPoint.pptx
This document discusses rational and irrational numbers. Rational numbers can be written as fractions with whole number numerators and denominators, and include terminating and repeating decimals. Irrational numbers cannot be written as fractions and are represented by non-terminating, non-repeating decimals like the square root of 2 or pi. Both rational and irrational numbers exist on the real number line, making up the set of real numbers.
4 ESO Academics - Unit 01 - Real Numbers and Percentages
Rational numbers can be expressed as fractions with integer numerators and denominators, while irrational numbers cannot. Some important irrational numbers include π, the square root of 2, the golden ratio φ, and e. Together, the sets of rational and irrational numbers form the set of real numbers, which can be represented on the real number line. Approximating numbers involves rounding them to a specified place value or number of significant figures.
Basic math concepts
An integer is a whole number that is not a fraction or decimal. Positive numbers are greater than zero, negative numbers are less than zero, and zero is neutral. Even numbers are divisible by 2, odd numbers are not. A number is prime if it is only divisible by 1 and itself. Distinct integers cannot have the same value. Divisibility rules can help determine if a number is divisible by other numbers without a calculator.
Classifying Real Numbers
This document classifies different types of real numbers. It defines real numbers as all numbers that can be graphed on a number line. Rational numbers are numbers that can be written as fractions or repeating decimals, while irrational numbers cannot. Integers are positive, negative, or zero whole numbers without fractions or decimals. Whole numbers are positive whole numbers without fractions or decimals, and natural numbers are only the positive whole numbers.
Radhika digital textbook
1. Rational numbers include integers and fractions, and can be written in the form x/y where x and y are integers.
2. Addition, subtraction, multiplication, and division of rational numbers can be performed by finding equivalent fractions with a common denominator or by using algebraic expressions.
3. Two fractions are equal if their numerators divided by their denominators are equal (i.e. if aq = bp, where a/b and p/q are the fractions).
Chap1_Number and Number Sydtem.pptx
The document provides an overview of different number systems including decimal, binary, octal, and hexadecimal systems. It discusses the following key points in 3 sentences:
The decimal system uses base 10 and the digits 0-9. The binary system uses base 2 and only the digits 0 and 1. The octal and hexadecimal systems use bases 8 and 16 respectively and have unique symbol sets in addition to 0-9 to represent values.
The-Real-Number-System.ppt
The real numbers are the set of numbers containing all of the rational numbers and all of the irrational numbers. The real numbers are “all the numbers” on the number line. There are infinitely many real numbers just as there are infinitely many in the other sets of numbers.
Real numbers ppt
Rational numbers can be written as fractions with an integer as the numerator and a non-zero integer as the denominator that do not share any common factors. Rational numbers can be represented by either terminating or repeating decimals. Between any two rational numbers, there exist two additional rational numbers. Irrational numbers cannot be expressed as a fraction with an integer numerator and denominator. Prime numbers are only divisible by 1 and themselves, while composite numbers are numbers greater than 1 that are not prime numbers.
[L1] NUMBER SYSTEM (6).pdf
Surabhi Gangwar has over 6 years of teaching experience and has mentored over 10,000 students, including 5,000 students for NTSE and Olympiad exams. She provides lessons on topics related to number systems, including natural numbers, whole numbers, integers, fractions, irrational numbers, real numbers, and rational numbers. She explains their properties and provides examples of representing them on a number line.
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みなさんこんにちはこれ何文字まで入るの？40文字以下不可とか本当に意味わからないけどこれ限界文字数書いてないからマジでやばい文字数いけるんじゃないの？えこ...
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Rational and irrational numbers by Kashae Alexander
- 1. Multiplying Rational and Irrational numbers Kashae` Alexander!
- 3. Examples 1/567, 34/12, or/and 12/144
- 4. To multiply rational numbers you have to convert them into a Decimal, and to do that let's start with 1/567*34/12 you divide the numerator by the denominator, so 1/567=.001763.... and 34/12=2.83333....
- 5. Now you multiply the Decimals of the fractions(1/567, and 34/12=?)or (0.001763*2.83333=.004995)
- 7. To multiply a Rational number and a Irrational number it haves to equal an irrational number, it is not possible for it to equal a rational number because a irrational number is not a fraction , and cannot be. For example
- 9. 3.14592654....*1/12=.2617993878... and that IS NOT a rational number, which remember is a fraction or CAN be a fraction. Which this answer CANNOT be made into a fraction.