College Algebra (6th Edition)

Published by Pearson
ISBN 10: 0-32178-228-3
ISBN 13: 978-0-32178-228-1

Chapter P - Prerequisites: Fundamental Concepts of Algebra - Exercise Set P.2: 130

Answer

If we have a number $N$ written in decimal notation ($N=7680.1$, for example), we can bring it into scientific notation using the form $N=a*10^n$, in which $a$ is a number with an absolute value between $1$ and $10$ (and including $1$), and $n$ is an integer. To convert the decimal to scientific notation, we first determine $a$, the numerical factor. Move the decimal point in the given number to get a number with an absolute value between $1$ and $10$ (including $1$). Finally, determine $n$, the exponent of $10$. This exponent is positive if the decimal place is moved to the left and negative if moved to the right, and it is $0$ if it is not moved at all. If we have $N=7680.1$, we move the decimal point three places to the left, so the exponent is $3$. The final scientific notation would be $N=7.6801*10^3$.

Work Step by Step

This is how to convert from decimal notation to scientific notation.
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