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Standard Form

This document provides an overview of standard form, also known as scientific notation, and its usage in mathematics. It covers the conversion of ordinary numbers into standard form, including examples of large and small numbers expressed succinctly. Readers will learn to perform calculations using numbers in standard form and how to manipulate them for practical applications, such as measuring distances and speeds. With clear definitions and examples, this guide is essential for mastering the use of standard form in various mathematical contexts.

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Standard Form

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  1. Standard Form 3 x 105 = 3 x 100 000 = 300 000 4.36 x 103 = 4.36 x 1 000 = 4360 Scientific Notation

  2. 10 000 000 = 10 7 10x10x10x10x10x10x10 1 000 000 = 10 6 100 000 = 10 5 10 000 = 10 4 or x 10 x 10 x 10 x 10 1000 = 10 3 or x 10 x 10 x 10 100 = 10 2 or x 10 x 10 10 = 10 1 or x 10 1 = 10 0 or x1 0.1 = 10 -1 or ÷10 0.01 = 10 -2 or ÷10 ÷10 0.001 = 10 -3 or ÷10 ÷10 ÷10 0.000 1 = 10 -4 or ÷10 ÷10 ÷10 ÷10 0.000 01 = 10 -5

  3. 1 2 3 4 5 250 000 = 2.5 x 10 x 10 x 10 x 10 x 10 25 250 2500 25 000 250 000 Standard Form 2.5 x 10 5 = 62 370 = 6.237 x10 4 3 162 = 3.162 x10 3 0.26 = 2.6 x10 -1

  4. Rewrite the following as ordinary numbers 7 x 10 4 4.39 x 10 6 7.21 x 10 0 3.2 x 10 -2 1.82 x 10 -5 5.09 x 10 -1 Give the following in Standard form: 569 2 817 539 270 5.69 x 10 2 2.817 x 10 3 5.3927 x 10 5 9.3 0.395 0.003 68 9.3 x 10 0 3.95 x 10 -1 3.68 x 10 -3 70 000 4 390 000 7.21 0.032 0.000 0182 0.509

  5. Calculating with numbers in standard form Distance of 3.6 x 107 kilometres at speed of 1.8 x 103 km/s 3.6 x 107 D S T T = 1.8 x 103 3.6 107 = 7 - 3 x 1.8 103 = 2 104 seconds x Speed of 3.27 x 102 m/sec for 1 hour 3.27 x 6 1952 x 6 117.12 D = 3.27 x 102x 60 x 60 = 3.27 x 6 x 6 x 10 2x 10 x 10 = 117.12 x 10 4 4 + 2 = 1.1712 x 10 6

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