Introductory Chemistry (5th Edition)

Published by Pearson
ISBN 10: 032191029X
ISBN 13: 978-0-32191-029-5

Chapter 2 - Measurement and Problem Solving - Exercises - Problems - Page 48: 39


Decimal Notation: 2,000,000,000; Scientific Notation: $2$$\times$$10^{9}$ Decimal Notation: 1,211,000,000; Scientific Notation: $1.211$$\times$$10^{9}$ Decimal Notation: 0.000874; Scientific Notation: $8.74$$\times$$10^{-4}$ Decimal Notation: 320,000,000,000; Scientific Notation: $3.2$$\times$$10^{11}$

Work Step by Step

To convert from decimal notation to scientific notation, place a decimal after the first nonzero value. For 2,000,000,000, place a decimal after the 2 and then move it over to the right as many times as needed until the correct amount of zeros are added as place fillers. The number of decimal movements is the exponent attached to the base power of 10. For 0.000874, place a decimal after the 8 so that 8.74 will have to be multipled by 10 to a negative power to bring it back to its decimal form. Move the decimal place over to the left, adding zeros as place fillers until the original value is reached. The number of decimal movements is the exponent needed for scientific notation. When converting from scientific notation to decimal notation, move the decimal place over to the left or right as indicated by the power attached to the base of 10. The decimal for 1.211 will be moved over 9 places to the right, adding zeros as necessary. The same can be done for 3.2, in which the decimal is moved over 11 times to the right.
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