Introductory Chemistry

Educators

RP

Problem 1

A _____ represents a quantitative observation.

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Problem 2

Although your textbook lists the rules for converting an ordinary number to scientific notation, oftentimes students remember such rules better if they put them into their own words. Pretend you are
helping your 12-year-old niece with her math homework, and write a paragraph explaining to her how
to convert the ordinary number 2421 to scientific notation.

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Problem 3

When a large or small number is written in standard scientific notation, the number is expressed as the
product of a number between 1 and 10, multiplied by the appropriate power of 10. For each of the following numbers, indicate what number between 1 and 10 would be appropriate when expressing the numbers in standard scientific notation.
$$\begin{array}{ll}{\text { a. } 9651} & {\text { c. } 93,241} \\ {\text { b. } 0.003521} & {\text { d. } 0.000001002}\end{array}$$

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Problem 4

When a large or small number is written in standard scientific notation, the number is expressed as the
product of a number between 1 and 10, multiplied by the appropriate power of 10. For each of the following numbers, indicate what power of 10 would be appropriate when expressing the numbers in standard scientific notation.
a. $82,350$
b. 0009375
c. 251
d. 0.0000000000000000000000000000009109

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Problem 5

Will the power of 10 have a positive or a negative exponent when each of the following numbers is rewritten in standard scientific notation?
$$\begin{array}{ll}{\text { a. } 42,751} & {\text { c. } 0.002045} \\ {\text { b. } 1253} & {\text { d. } 0.1089}\end{array}$$

RP
Ronald P.

Problem 6

Will the power of 10 have a positive, negative, or zero exponent when each of the following numbers is
rewritten in standard scientific notation?
$$\begin{array}{ll}{\text { a. } 0.9091} & {\text { c. } 9091} \\ {\text { b. } 9.091} & {\text { d. } 0.00000009091}\end{array}$$

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Problem 7

Express each of the following numbers in standard scientific notation.
a. 0.5012
b. $5,012,000$
C. 0.000005012
d. 5.012
e. 5012
f. 0.005012

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Problem 8

Rewrite each of the following as an “ordinary” decimal number.
a. $2.789 \times 10^{3}$
b. $2.789 \times 10^{-3}$
c. $9.3 \times 10^{7}$
d. $4.289 \times 10^{1}$
e. $9.999 \times 10^{4}$
f. $9.999 \times 10^{-5}$

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Problem 9

By how many places must the decimal point be moved, and in which direction, to convert each of
the following to “ordinary” decimal numbers?
a. $4.311 \times 10^{6}$
b. $7.895 \times 10^{-5}$
c. $8.712 \times 10^{1}$
d. $4.995 \times 10^{0}$
e. $2.331 \times 10^{18}$
f. $1.997 \times 10^{-16}$

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Problem 10

By how many places must the decimal point be moved, and in which direction, to convert each of
the following to standard scientific notation?
a. 5993
b. $-72.14$
c. 0.00008291
d. 62.357
e. 0.01014
f. 324.9

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Problem 11

Write each of the following numbers in standard scientific notation.
a. $97,820$
b. $42.14 \times 10^{3}$
c. $0.08214 \times 10^{-3}$
d. 0.0003914
e. 927.1
f. $4.781 \times 10^{2} \times 10^{-3}$

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Problem 12

Write each of the following numbers as “ordinary” decimal numbers.
a. $6.244 \times 10^{3}$
b. $9.117 \times 10^{-2}$
c. $8.299 \times 10^{1}$
d. $1.771 \times 10^{-4}$
e. $5.451 \times 10^{2}$
f. $2.934 \times 10^{-5}$

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Problem 13

Write each of the following numbers in standard scientific notation.
a. 1$/ 1033$
b. 1$/ 10^{5}$
c. 1$/ 10^{-7}$
d. 1$/ 0.0002$
e. $1 / 3,093,000$
f. 1$/ 10^{-4}$
g. 1$/ 10^{9}$
h. 1$/ 0.000015$

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Problem 14

Write each of the following numbers in standard scientific notation.
a. 1$/ 0.00032$
b. $10^{3} / 10^{-3}$
c. $10^{3} / 10^{3}$
d. $1 / 55,000$
e. $\left(10^{5}\right)\left(10^{4}\right)\left(10^{-4}\right) /\left(10^{-2}\right)$
f. 43.2$/\left(4.32 \times 10^{-5}\right)$
g. $\left(4.32 \times 10^{-5}\right) / 432$
h. 1$/\left(10^{5}\right)\left(10^{-6}\right)$

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