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: 72


\[6.47\times {{10}^{-7}}\].

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 \[0.000000647\]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 \[0.000000647\], as provided number is less than \[1\]. So, \[a=6.47\]. Again, the decimal point moves \[7\] places right in \[0.000000647\], so\[n=-7\]. Hence the scientific notation of the real number \[0.000000647\]is \[6.47\times {{10}^{-7}}\]. Expression of \[0.000000647\]in scientific notation is \[6.47\times {{10}^{-7}}\].
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