What is Standard Form

What is Standard Form What is Standard Form Standard form is a way of writing down very large or very small numbers easily. 103 = 1000, so 4 × 103 = 4000 . So 4000 can be written as 4 × 10³ . This idea can be used to write even larger numbers down easily in standard form. Small numbers can also be written in standard form. However, instead of the index being positive (in the above example, the index was 3), it will be negative. The rules when writing a number in standard form is that first you write down a number between 1 and 10, then you write × 10(to the power of a number). Example Write 81 900 000 000 000 in standard form: 81 900 000 000 000 = 8.19 × 1013 It’s 1013 because the decimal point has been moved 13 places to the left to get the number to be 8.19 Example Know More About The Product Rule Math.Tutorvista.com

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Write 0.000 001 2 in standard form: 0.000 001 2 = 1.2 × 10-6 It’s 10-6 because the decimal point has been moved 6 places to the right to get the number to be 1.2 On a calculator, you usually enter a number in standard form as follows: Type in the first number (the one between 1 and 10). Press EXP . Type in the power to which the 10 is risen. Manipulation in Standard Form This is best explained with an example: Example : The number p written in standard form is 8 × 105 The number q written in standard form is 5 × 10-2 Calculate p × q. Give your answer in standard form. Multiply the two first bits of the numbers together and the two second bits together: 8 × 5 × 105 × 10-2, = 40 × 103 (Remember 105 × 10-2 = 103) The question asks for the answer in standard form, but this is not standard form because the first part (the 40) should be a number between 1 and 10. = 4 × 104,

Calculate p ÷ q.

Give your answer in standard form. This time, divide the two first bits of the standard forms. Divide the two second bits. (8 ÷ 5) × (105 ÷ 10-2) = 1.6 × 107 Learn More Instantaneous Rate of Change Formula Math.Tutorvista.com

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Factor Polynomials Factor Polynomials Factoring Polynomials refers to factoring a polynomial into irreducible polynomials over a given field. It gives out the factors that together form a polynomial function. A polynomial function is of the form xn + xn -1 + xn - 2 + . . . . + k = 0, where k is a constant and n is a power. Polynomials are expressions that are formed by adding or subtracting several variables called monomials. Monomials are variables that are formed with a constant and a variable of some degree. Examples of monomials are 5x3, 6a2. Monomials having different exponents such as 5x3 and 3x4 cannot be added or subtracted but can be multiplied or divided by them. Any polynomial of the form F(a) can also be written as Learning how to factor polynomials does not have to be difficult. GradeA will break down the steps for you, show you simple examples with visual illstrations, and also give you some clever tips and tricks.

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Example 2: Factor the trinomial 9x 2 + 3x - 2 Solution : To factor the above trinomial, we need to write it in the form. 9x 2 + 3x - 2 = (ax + m)(bx + n) Expand the product on the right above 9x 2 + 3x - 2 = abx 2 + x(mb + na) + mn For the polynomial on the left to be equal to the polynomial on the right we need to have equal corresponding coefficients, hence Ab = 9 , mb + na = 3, mn = -2 Trial values for a and b are: a = 1 and b = 9 or a = 3 and b = 3 Trial values for m and n are: m = 1 and n = -2, m = 2 and n = -1, m = -1 and n = 2 and m = -2 and n = 1. Trying various values for a, b, m and n among the list above, we arrive at: 9x 2 + 3x - 2 = (3x + 2)(3x - 1) As a practice, multiply (3x + 2)(3x - 1) and simplify to obtain the given trinomial.