Negative index notation pdf

For information about these resources and an index for the whole collectio. Negative refractive index materials article pdf available in journal of computational and theoretical nanoscience 32. The number is now between 1 and and the power of 10 is 9. Notes on summations and related topics james aspnes. An expression with a negative index is the reciprocal of the expression with positive index.

The topic of indices from the gcse books of the mathematics enhancement program. Notes on scientific notation and significant figures prepared by dr. A worksheet for practising the use of negative indices. Exponents in the real world passys world of mathematics. Index notation january 10, 20 one of the hurdles to learning general relativity is the use of vector indices as a calculational tool. In activity 2, they will multiply and divide exponents. In this section of text you will learn about powers and rules for manipulating them through a number of worked examples. Indices, law, rule, power, integer, standard form, ten, positive, negative, large, small, decimal, fractional. The fact that qis negative means that the image is virtual on same side as object. For the warm up, students will solve a problem about brain cells. The variable iis called the index of summation, ais the lower bound or lower limit, and bis the upper bound or upper limit. Our mission is to provide a free, worldclass education to anyone, anywhere. Introduction to tensor calculus a scalar eld describes a onetoone correspondence between a single scalar number and a point.

Use of a power or index is simply a form of notation, that is, a way of writing something down. Scientific notation is also used for expressing very small decimal values like the size of flu virus molecules, or the distance between atoms in a crystal structure. In several programming languages, index notation is a way of addressing elements of an array. The symbolic notation v and index notation viei or simply vi can be used to denote a vector. The 2 in y 2 is called the power or index, and y is the base. To express this decimal in scientific notation, one has to. The notation itself sigma notation is a way of writing a sum of many terms, in a concise form. When you multiply two pronumerals together, or multiply a pronumeral to itself by a certain number of times, we write the expression in an index form for the repeated pronumeral. The index laws in arithmetic with nonzero whole number indices.

Then use the index laws and express the answer with positive indices. We should move the decimal point 2 places to the left. Negativeindex metamaterial or negativeindex material nim is a metamaterial whose refractive index for an electromagnetic wave has a negative value over some frequency range nims are constructed of periodic basic parts called unit cells, which are usually significantly smaller than the wavelength of the externally applied electromagnetic radiation. Students can solve simple expressions involving exponents, such as 3 3, 12 4, 5 0, or 82, or write multiplication expressions using an exponent.

Use index notation involving fractional, negative and zero powers. Negative scientific notation is expressing a number that is less than one, or is a decimal with the power of 10 and a negative exponent. We saw the importance of the index laws when dealing with powers in. Guys please help, i have a maths topics test tomm and im dying here. They help us to complete problems involving powers more easily. Tensors and invariants tensorindex notation scalar 0th order tensor, usually we consider scalar elds function of space and time. Indices, index notation mep gcse activities teaching resources. Mathematicians invented this notation centuries ago because they didnt. Masingale, le moyne college department of chemistry. An online presentation of this lesson is available on slideshare at the following link.

Scientific notation also referred to as scientific form or standard index form, or standard form in the uk is a way of expressing numbers that are too big or too small to be conveniently written in decimal form. Consider the vectorsa andb, which can be expressed using index notation as a a 1. This includes converting expressions into index notation form and calculating values both with and without a calculator. We saw the importance of the index laws when dealing with powers in the module, multiples, factors and powers. Index notation worksheets practice questions and answers.

The exponent or index or power of a number says how many times to use the number in a multiplication. We treat negative indices in calculations in the same manner as positive indices. Notes on summations and related topics yale university. Negative numbers dont have square roots because a square is either positive or zero. It becomes easier to visualize what the different terms in equations mean. In activity 3, they will practice scientific notation. Literacy activities find a word study stack quizlet crossword fill in the blanks. This worksheet features converting negative indices into fractions and viceversa as well as converting decimals into index notation. One free index, as here, indicates three separate equations. Chapter 36 lenses a powerpoint presentation by paul e.

Well now look at how we can use them to execute various mathematical calculations, such as multiplication and division. Each lesson contains a starter, examples, top tips, exercises, exam practices and even a plenary. Using index notation, we can express the vector a as. The index can be any positive or negative number or zero. Whileyouwilleventuallylearntensornotationthatbypassessomeoftheindexusage,theessentialformof calculationsoftenremainsthesame.

A worksheet for practising the use of index notation powers. Algebraic fractions manipulate algebraic fractions where the numerator andor the denominator can be numeric, linear or quadratic. One of the hurdles to learning general relativity is the use of vector indices as a calculational tool. This method is used since it is closest to how it is implemented in assembly language whereby the address of the first element is used as a base, and a multiple the index of the element size is. Fluid mechanics, sg2214, ht20 september 4, 20 exercise 1. The large jagged symbol is a stretchedout version of a capital greek letter sigma. Understanding and solving exponents, radicals, and scientific notation without algebra. In activity 1, they will add and subtract exponents. These first four sections of this module provide all the skills needed to solve straightforward linear equations, without the constraints of avoiding negative coefficients. An example of a number that is less than one is the decimal 0. Matrix and index notation david roylance department of materials science and engineering massachusetts institute of technology cambridge, ma 029. This pack contains a power point that is broken up into two lessons which covers index notation and fractional indices.

This is a complete lesson on index notation that covers how to write and interpret numbers written in index form. For this reason, it is essential to use a shorthand notation called the index notation1. Index notation, also commonly known as subscript notation or tensor notation, is an extremely useful tool for performing vector algebra. It is commonly used by scientists, mathematicians and engineers, in part because it can simplify certain arithmetic operations. Zero and negative indices index notation wjec gcse.

Index notation has the dual advantages of being more concise and more transparent. The pythagoreans thought of number as a multitude of units. Clearly the index laws need to be integrated into algebra. Index notation wjec indices are a way of representing numbers and letters that have been multiplied by themselves a number of times. Index notationpowers free worksheets, powerpoints and. Scientific notation all numbers, regardless of magnitude, can be expressed in the form. Indices or powers mctyindicespowers20091 a knowledge of powers, or indices as they are often called, is essential for an understanding of most algebraic processes. On scientific calculators it is usually known as sci. Online presentation on exponents in the real world. The pack contains a full lesson plan, along with accompanying resources, including a student worksheet and suggested support and extension activities. We saw in index notation in prealgebra on how to represent numbers using basic index notation.

Identities and proof use algebra to support and construct proofs surds. Scientific notation is a standardized method of representing extremely large or extremely small numbers in simple exponential terms that are written as the product of a real number and a power of 10. Mathematics linear 1ma0 fractional and negative indices. In this work, i gently introduce index notation, moving through using the summation convention. To simplify algebraic expressions, remove the brackets first. In the next two examples we start with an expression which has a negative index, and rewrite it so that it has a positive index, using the rule a. Please define negative index short and simple not too complicated. Exponents, radicals, and scientific notation prealgebra. Mathematics linear 1ma0 fractional and negative indices materials required for examination items included with question papers ruler graduated in centimetres and nil millimetres, protractor, compasses, pen, hb pencil, eraser. Create an unlimited supply of worksheets for practicing exponents and powers. Indexing is one of the most fundamental concept in mathematical notation.

Index notation worksheets for gcse foundation and gcse higher. The miller indices can be used to specify directions and planes in a crystal ashcroft76,kittel96. Different types of numerical indices represent different types of mathematics and this guide looks at. X5 k1 3k the sigma indicates that a sum is being taken. An ndimensional vector eld is described by a onetoone correspondence between nnumbers and a point.