Chemistry (7th Edition)

Published by Pearson
ISBN 10: 0321943171
ISBN 13: 978-0-32194-317-0

Chapter 1 - Chemical Tools: Experimentation and Measurement - Worked Example - Page 7: 1

Answer

(a) Scientific notation: $5 \times 10^{-9}$ $m$ Appropriate prefix: $5$ $nm$ (b) Scientific notation: $4.0075017 \times 10^{7}$ $m$ Appropriate prefix: $40.075017$ $Mm$

Work Step by Step

(a) To write the quantity in scietific notation, we have to move the decimal point to the right of the first number different than 0.(Counting from the left to the right.) In 0.000000005, this number is "5"; therefore, we should put the decimal point to the right of it. 5. Notice that we had to move the point by 9 times to the right; therefore, we should put a "$\times 10^{-9}$" at the end. $5 \times 10^{-9}$ $m$ Now, identify the closest prefix to $10^{-9}$: it is nano "n." Therefore: $5$ $nm$ (nanometers) (b) In 40,075,017 the first non-neutral number is "4"; therefore, we should put the decimal point between it and the zero. $4.0075017$. Notice that we moved the decimal point by 7 times to the left; therefore, we should put a "$\times 10^7$" at the end. $4.0075017 \times 10^{7}$ $m$ Identify the closest prefix to $10^7$; it is mega "M", which has the value of $10^6$. Therefore: $4.0075017 \times \frac{10^7}{10^6}$ $Mm$ (Megameters) $4.0075017 \times 10$ $Mm$ (Megameters) $40.075017$ $Mm$ (Megameters)
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