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This module is from Elementary Algebra by Denny Burzynski and Wade Ellis, Jr. The basic operations with real numbers are presented in this chapter. The concept of absolute value is discussed both geometrically and symbolically. The geometric presentation offers a visual understanding of the meaning of |x|. The symbolic presentation includes a literal explanation of how to use the definition. Negative exponents are developed, using reciprocals and the rules of exponents the student has already learned. Scientific notation is also included, using unique and real-life examples.Objectives of this module: be able to convert a number from standard form to scientific form and from scientific form to standard form, be able to work with numbers in scientific notation.

Overview

  • Standard Form to Scientific Form
  • Scientific Form to Standard Form
  • Working with Numbers in Scientific Notation

Standard form to scientific form

Very large numbers such as 43,000,000,000,000,000,000 (the number of different possible configurations of Rubik’s cube) and very small numbers such as 0.000000000000000000000340 (the mass of the amino acid tryptophan) are extremely inconvenient to write and read. Such numbers can be expressed more conveniently by writing them as part of a power of 10.

To see how this is done, let us start with a somewhat smaller number such as 2480. Notice that

2480 Standard form = 248.0 × 10 1 = 24.80 × 10 2 = 2.480 × 10 3 Scientific form

Scientific form

The last form is called the scientific form of the number. There is one nonzero digit to the left of the decimal point and the absolute value of the exponent on 10records the number of places the original decimal point was moved to the left .

0.00059 = 0.0059 10 = 0.0059 10 1 = 0.0059 × 10 1 = 0.059 100 = 0.059 10 2 = 0.059 × 10 2 = 0.59 1000 = 0.59 10 3 = 0.59 × 10 3 = 5.9 10 , 000 = 5.9 10 4 = 5.9 × 10 4

There is one nonzero digit to the left of the decimal point and the absolute value of the exponent of 10 records the number of places the original decimal point was moved to the right .

Scientific notation

Numbers written in scientific form are also said to be written using scientific notation. In scientific notation , a number is written as the product of a number between and including 1 and 10 ( 1 is included, 10 is not ) and some power of 10.

Writing a number in scientific notation

To write a number in scientific notation:
  1. Move the decimal point so that there is one nonzero digit to its left.
  2. Multiply the result by a power of 10 using an exponent whose absolute value is the number of places the decimal point was moved. Make the exponent positive if the decimal point was moved to the left and negative if the decimal point was moved to the right.

Sample set a

Write the numbers in scientific notation.

981

The number 981 is actually 981. , and it is followed by a decimal point. In integers, the decimal point at the end is usually omitted.

981 = 981. = 9.81 × 10 2

The decimal point is now two places to the left of its original position, and the power of 10 is 2.

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54.066 = 5.4066 × 10 1 = 5.4066 × 10

The decimal point is one place to the left of its original position, and the power of 10 is 1.

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Source:  OpenStax, Elementary algebra. OpenStax CNX. May 08, 2009 Download for free at http://cnx.org/content/col10614/1.3
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