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.

Check back soon!

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.

$$\begin{array}{ll}{\text { a. } 9651} & {\text { c. } 93,241} \\ {\text { b. } 0.003521} & {\text { d. } 0.000001002}\end{array}$$

Check back soon!

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

Check back soon!

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}

$$

Ronald P.

Numerade Educator

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}

$$

Check back soon!

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

Check back soon!

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. $9.999 \times 10^{-5}$

Check back soon!

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. $1.997 \times 10^{-16}$

Check back soon!

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

Check back soon!

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. $4.781 \times 10^{2} \times 10^{-3}$

Check back soon!

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. $2.934 \times 10^{-5}$

Check back soon!

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$/ 0.000015$

Check back soon!

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$/\left(10^{5}\right)\left(10^{-6}\right)$

Check back soon!