These first four sections of this module provide all the skills needed to solve straightforward linear equations, without the constraints of avoiding negative coefficients. The symbolic notation v and index notation viei or simply vi can be used to denote a vector. It becomes easier to visualize what the different terms in equations mean. An online presentation of this lesson is available on slideshare at the following link. On scientific calculators it is usually known as sci. Each lesson contains a starter, examples, top tips, exercises, exam practices and even a plenary. Whileyouwilleventuallylearntensornotationthatbypassessomeoftheindexusage,theessentialformof calculationsoftenremainsthesame. The 2 in y 2 is called the power or index, and y is the base. 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. An example of a number that is less than one is the decimal 0. The variable iis called the index of summation, ais the lower bound or lower limit, and bis the upper bound or upper limit. The exponent or index or power of a number says how many times to use the number in a multiplication. Exponents, radicals, and scientific notation prealgebra. 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.
The pack contains a full lesson plan, along with accompanying resources, including a student worksheet and suggested support and extension activities. We saw the importance of the index laws when dealing with powers in the module, multiples, factors and powers. Fluid mechanics, sg2214, ht20 september 4, 20 exercise 1. The index laws in arithmetic with nonzero whole number indices. Understanding and solving exponents, radicals, and scientific notation without algebra. Consider the vectorsa andb, which can be expressed using index notation as a a 1. To simplify algebraic expressions, remove the brackets first. Index notation worksheets practice questions and answers. For this reason, it is essential to use a shorthand notation called the index notation1. Please define negative index short and simple not too complicated.
There are no indications of negative numbers in their work. A worksheet for practising the use of index notation powers. They help us to complete problems involving powers more easily. Chapter 36 lenses a powerpoint presentation by paul e. We saw in index notation in prealgebra on how to represent numbers using basic index notation. We should move the decimal point 2 places to the left. Then use the index laws and express the answer with positive indices. This pack contains a power point that is broken up into two lessons which covers index notation and fractional indices. Indices, law, rule, power, integer, standard form, ten, positive, negative, large, small, decimal, fractional.
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. Index notation worksheets for gcse foundation and gcse higher. Zero and negative indices index notation wjec gcse. Masingale, le moyne college department of chemistry. The fact that qis negative means that the image is virtual on same side as object. 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. 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 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. Negative refractive index materials article pdf available in journal of computational and theoretical nanoscience 32. Create an unlimited supply of worksheets for practicing exponents and powers.
Introduction to tensor calculus a scalar eld describes a onetoone correspondence between a single scalar number and a point. 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. Index notationpowers free worksheets, powerpoints and. For the warm up, students will solve a problem about brain cells. Indices or powers mctyindicespowers20091 a knowledge of powers, or indices as they are often called, is essential for an understanding of most algebraic processes. Mathematicians invented this notation centuries ago because they didnt.
Notes on summations and related topics james aspnes. Index notation january 10, 20 one of the hurdles to learning general relativity is the use of vector indices as a calculational tool. Use index notation involving fractional, negative and zero powers. Indexing is one of the most fundamental concept in mathematical notation. One free index, as here, indicates three separate equations. 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. Well now look at how we can use them to execute various mathematical calculations, such as multiplication and division. Guys please help, i have a maths topics test tomm and im dying here. The miller indices can be used to specify directions and planes in a crystal ashcroft76,kittel96. Index notation worksheet 1 introduces indices at grade 3, index notation worksheet 2 and index notation worksheet 3 asks students to calculate in index notation working at grade 4 and grade 6. Index notation 3 the scalar product in index notation we now show how to express scalar products also known as inner products or dot products using index notation. We saw the importance of the index laws when dealing with powers in.
The miller indices of a plane are defined in the following way. This is a complete lesson on index notation that covers how to write and interpret numbers written in index form. In this section of text you will learn about powers and rules for manipulating them through a number of worked examples. Notes on scientific notation and significant figures prepared by dr. Online presentation on exponents in the real world. This worksheet features converting negative indices into fractions and viceversa as well as converting decimals into index notation. In several programming languages, index notation is a way of addressing elements of an array. The index can be any positive or negative number or zero. We treat negative indices in calculations in the same manner as positive indices. Scientific notation all numbers, regardless of magnitude, can be expressed in the form. When the indices of pronumerals are negative, we get a negative indices. It is commonly used by scientists, mathematicians and engineers, in part because it can simplify certain arithmetic operations.
The worksheets can be made in html or pdf format both are easy to print. Notes on summations and related topics yale university. Negative numbers dont have square roots because a square is either positive or zero. Our mission is to provide a free, worldclass education to anyone, anywhere. Literacy activities find a word study stack quizlet crossword fill in the blanks. In activity 1, they will add and subtract exponents. An expression with a negative index is the reciprocal of the expression with positive index. 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. Algebraic fractions manipulate algebraic fractions where the numerator andor the denominator can be numeric, linear or quadratic. Index notation in mathematics and modelling language lpl.
For information about these resources and an index for the whole collectio. Identities and proof use algebra to support and construct proofs surds. This includes converting expressions into index notation form and calculating values both with and without a calculator. Note that all the earlier index laws also hold for negative indices. Exponents in the real world passys world of mathematics. The notation itself sigma notation is a way of writing a sum of many terms, in a concise form. Index notation has the dual advantages of being more concise and more transparent. Using index notation, we can express the vector a as. The pythagoreans thought of number as a multitude of units. Different types of numerical indices represent different types of mathematics and this guide looks at. Mathematics linear 1ma0 fractional and negative indices. Index notation wjec indices are a way of representing numbers and letters that have been multiplied by themselves a number of times.
The large jagged symbol is a stretchedout version of a capital greek letter sigma. One of the hurdles to learning general relativity is the use of vector indices as a calculational tool. An ndimensional vector eld is described by a onetoone correspondence between nnumbers and a point. The topic of indices from the gcse books of the mathematics enhancement program. 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. Indices, index notation mep gcse activities teaching resources. In activity 2, they will multiply and divide exponents. To express this decimal in scientific notation, one has to.
The number is now between 1 and and the power of 10 is 9. In this work, i gently introduce index notation, moving through using the summation convention. Index notation, also commonly known as subscript notation or tensor notation, is an extremely useful tool for performing vector algebra. In activity 3, they will practice scientific notation. Matrix and index notation david roylance department of materials science and engineering massachusetts institute of technology cambridge, ma 029. A worksheet for practising the use of negative indices. Tensors and invariants tensorindex notation scalar 0th order tensor, usually we consider scalar elds function of space and time. X5 k1 3k the sigma indicates that a sum is being taken. Clearly the index laws need to be integrated into algebra.