Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 5 - Number Theory and the Real Number System - 5.6 Exponents and Scientific Notation - Exercise Set 5.6 - Page 320: 71


\[2.93\times {{10}^{-6}}\].

Work Step by Step

Any real number in the form \[a\times {{10}^{n}}\] is said to be in the scientific notation, where \[1\le a<10\], and n is any integer. Since, the provided real number \[0.00000293\]is less than \[1\], so n must be negative in the scientific notation \[a\times {{10}^{n}}\]. To determine the value of a, move the decimal point from left to right in the provided real number \[0.00000293\], as provided number is less than \[1\]. So, \[a=2.93\]. Again, the decimal point moves \[6\] places right in \[0.00000293\], so\[n=-6\]. Hence the scientific notation of the real number \[0.00000293\]is \[2.93\times {{10}^{-6}}\]. Expression of \[0.00000293\]in scientific notation is \[2.93\times {{10}^{-6}}\].
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