



The steps are summarized below.
Convert scientific notation to decimal form.
To convert scientific notation to decimal form:
 Determine the exponent,
$n$ , on the factor 10.
 Move the decimal
$n$ places, adding zeros if needed.
 If the exponent is positive, move the decimal point
$n$ places to the right.
 If the exponent is negative, move the decimal point
$\leftn\right$ places to the left.
 Check.
Multiply and divide using scientific notation
Astronomers use very large numbers to describe distances in the universe and ages of stars and planets. Chemists use very small numbers to describe the size of an atom or the charge on an electron. When scientists perform calculations with very large or very small numbers, they use scientific notation. Scientific notation provides a way for the calculations to be done without writing a lot of zeros. We will see how the Properties of Exponents are used to multiply and divide numbers in scientific notation.
Multiply. Write answers in decimal form:
$\left(4\phantom{\rule{0.2em}{0ex}}\times \phantom{\rule{0.2em}{0ex}}{10}^{5}\right)\left(2\phantom{\rule{0.2em}{0ex}}\times \phantom{\rule{0.2em}{0ex}}{10}^{\mathrm{7}}\right).$
Solution
$\begin{array}{cccc}& & & \left(4\phantom{\rule{0.2em}{0ex}}\times \phantom{\rule{0.2em}{0ex}}{10}^{5}\right)\left(2\phantom{\rule{0.2em}{0ex}}\times \phantom{\rule{0.2em}{0ex}}{10}^{\mathrm{7}}\right)\hfill \\ \\ \\ \text{Use the Commutative Property to rearrange the factors.}\hfill & & & 4\xb72\xb7{10}^{5}\xb7{10}^{\mathrm{7}}\hfill \\ \\ \\ \text{Multiply.}\hfill & & & 8\phantom{\rule{0.2em}{0ex}}\times \phantom{\rule{0.2em}{0ex}}{10}^{\mathrm{2}}\hfill \\ \\ \\ \text{Change to decimal form by moving the decimal two places left.}\hfill & & & 0.08\hfill \end{array}$
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Multiply
$\left(3\phantom{\rule{0.2em}{0ex}}\times \phantom{\rule{0.2em}{0ex}}{10}^{6}\right)\left(2\phantom{\rule{0.2em}{0ex}}\times \phantom{\rule{0.2em}{0ex}}{10}^{\mathrm{8}}\right)$ . Write answers in decimal form.
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Multiply
$\left(3\phantom{\rule{0.2em}{0ex}}\times \phantom{\rule{0.2em}{0ex}}{10}^{\mathrm{2}}\right)\left(3\phantom{\rule{0.2em}{0ex}}\times \phantom{\rule{0.2em}{0ex}}{10}^{\mathrm{1}}\right)$ . Write answers in decimal form.
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Divide. Write answers in decimal form:
$\frac{9\phantom{\rule{0.2em}{0ex}}\times \phantom{\rule{0.2em}{0ex}}{10}^{3}}{3\phantom{\rule{0.2em}{0ex}}\times \phantom{\rule{0.2em}{0ex}}{10}^{\mathrm{2}}}.$
Solution
$\begin{array}{cccc}& & & \frac{9\phantom{\rule{0.2em}{0ex}}\times \phantom{\rule{0.2em}{0ex}}{10}^{3}}{3\phantom{\rule{0.2em}{0ex}}\times \phantom{\rule{0.2em}{0ex}}{10}^{\mathrm{2}}}\hfill \\ \\ \\ \text{Separate the factors, rewriting as the product of two fractions.}\hfill & & & \frac{9}{3}\phantom{\rule{0.2em}{0ex}}\times \phantom{\rule{0.2em}{0ex}}\frac{{10}^{3}}{{10}^{\mathrm{2}}}\hfill \\ \\ \\ \text{Divide.}\hfill & & & 3\phantom{\rule{0.2em}{0ex}}\times \phantom{\rule{0.2em}{0ex}}{10}^{5}\hfill \\ \\ \\ \text{Change to decimal form by moving the decimal five places right.}\hfill & & & \mathrm{300,000}\hfill \end{array}$
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Divide
$\frac{8\phantom{\rule{0.2em}{0ex}}\times \phantom{\rule{0.2em}{0ex}}{10}^{4}}{2\phantom{\rule{0.2em}{0ex}}\times \phantom{\rule{0.2em}{0ex}}{10}^{\mathrm{1}}}$ . Write answers in decimal form.
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Divide
$\frac{8\phantom{\rule{0.2em}{0ex}}\times \phantom{\rule{0.2em}{0ex}}{10}^{2}}{4\phantom{\rule{0.2em}{0ex}}\times \phantom{\rule{0.2em}{0ex}}{10}^{\mathrm{2}}}$ . Write answers in decimal form.
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Key concepts

Property of Negative Exponents
 If
$n$ is a positive integer and
$a\ne 0$ , then
$\frac{1}{{a}^{\text{\u2212}n}}={a}^{n}$

Quotient to a Negative Exponent
 If
$a,b$ are real numbers,
$b\ne 0$ and
$n$ is an integer , then
${\left(\frac{a}{b}\right)}^{\text{\u2212}n}={\left(\frac{b}{a}\right)}^{n}$

To convert a decimal to scientific notation:
 Move the decimal point so that the first factor is greater than or equal to 1 but less than 10.
 Count the number of decimal places,
$n$ , that the decimal point was moved.
 Write the number as a product with a power of 10. If the original number is:
 greater than 1, the power of 10 will be
${10}^{n}$
 between 0 and 1, the power of 10 will be
${10}^{\text{\u2212}n}$
 Check.

To convert scientific notation to decimal form:
 Determine the exponent,
$n$ , on the factor 10.
 Move the decimal
$n$ places, adding zeros if needed.
 If the exponent is positive, move the decimal point
$n$ places to the right.
 If the exponent is negative, move the decimal point
$\leftn\right$ places to the left.
 Check.
Questions & Answers
Bruce drives his car for his job. The equation R=0.575m+42 models the relation between the amount in dollars, R, that he is reimbursed and the number of miles, m, he drives in one day. Find the amount Bruce is reimbursed on a day when he drives 220 miles.
LeBron needs 150 milliliters of a 30% solution of sulfuric acid for a lab experiment but only has access to a 25% and a 50% solution. How much of the 25% and how much of the 50% solution should he mix to make the 30% solution?
hey everyone how to do algebra
Felecia answer 1.5 hours before he reaches her
I would like to solve the problem 6/2x
Does the x represent a number or does it need to be graphed ?
latonya
Arnold invested $64,000, some at 5.5% interest and the rest at 9%. How much did he invest at each rate if he received $4,500 in interest in one year?
Tickets for the community fair cost $12 for adults and $5 for children. On the first day of the fair, 312 tickets were sold for a total of $2204. How many adult tickets and how many child tickets were sold?
Threefourths of the people at a concert are children. If there are 87 children, what is the total number of people at the concert?
Erica earned a total of $50,450 last year from her two jobs. The amount she earned from her job at the store was $1,250 more than four times the amount she earned from her job at the college. How much did she earn from her job at the college?
Tsimmuaj
Erica earned a total of $50,450 last year from her two jobs. The amount she earned from her job at the store was $1,250 more than four times the amount she earned from her job at the college. How much did she earn from her job at the college?
Tsimmuaj
? Is there anything wrong with this passage
I found the total sum for 2 jobs, but found why elaborate on extra
If I total one week from the store *4 would = the month than the total is = x than x can't calculate 10 month of a year
candido
what would be wong
candido
87 divided by 3 then multiply that by 4. 116 people total.
Melissa
the actual number that has 3 out of 4 of a whole pie
candido
was having a hard time finding
Teddy
use Matrices for the 2nd question
Daniel
One number is 11 less than the other number. If their sum is increased by 8, the result is 71. Find the numbers.
26 + 37 = 63 + 8 = 71
gayla
how do we know the answer is correct?
Thisha
23 is 11 less than 37. 23+37=63.
63+8=71. that is what the question asked for.
gayla
23 +11 = 37. 23+37=63
63+8=71
Gayla
by following the question. one number is 11 less than the other number 26+11=37 so 26+37=63+8=71
Gayla
your answer did not fit the guidelines of the question 11 is 41 less than 52.
gayla
71811 =52 is this correct?
Ruel
let the number is 'x' and the other number is "x11". if their sum is increased means: x+(x11)+8 result will be 71. so
x+(x11)+8=71
2x11+8=71
2x3=71
2x=71+3
2x=74
1/2(2x=74)1/2
x=37 final answer
tesfu
Amara currently sells televisions for company A at a salary of $17,000 plus a $100 commission for each television she sells. Company B offers her a position with a salary of $29,000 plus a $20 commission for each television she sells. How televisions would Amara need to sell for the options to be equal?
company A 13 company b 5.
A 17,000+13×100=29,100
B 29,000+5×20=29,100
gayla
need help with math to do tsi test
Toocute
have you tried the TSI practice test ***tsipracticetest.com
gayla
DaMarcus and Fabian live 23 miles apart and play soccer at a park between their homes. DaMarcus rode his bike for 34 of an hour and Fabian rode his bike for 12 of an hour to get to the park. Fabian’s speed was 6 miles per hour faster than DaMarcus’s speed. Find the speed of both soccer players.
DaMarcus: 16 mi/hr
Fabian: 22 mi/hr
Sherman
Joy is preparing 20 liters of a 25% saline solution. She has only a 40% solution and a 10% solution in her lab. How many liters of the 40% solution and how many liters of the 10% solution should she mix to make the 25% solution?
32 is 40% , & 8 is 10 % , & any 4 letters is 5%.
Karen
It felt that something is missing on the question like:
40% of what solution?
10% of what solution?
Jhea
3% & 2% to complete the 25%
Sparcast
because she already has 20 liters.
Sparcast
ok I was a little confused I agree 15% & 5%
Sparcast
Jim and Debbie earned $7200. Debbie earned $1600 more than Jim earned. How much did they earned
Bebbie: 4,400 Jim: 2,800
Jhea
A river cruise boat sailed 80 miles down the Mississippi River for 4 hours. It took 5 hours to return. Find the rate of the cruise boat in still water and the rate of the current.
A veterinarian is enclosing a rectangular outdoor running area against his building for the dogs he cares for. He needs to maximize the area using 100 feet of fencing. The quadratic equation A=x(100−2x) gives the area, A , of the dog run for the length, x , of the building that will border the dog run. Find the length of the building that should border the dog run to give the maximum area, and then find the maximum area of the dog run.
Source:
OpenStax, Elementary algebra. OpenStax CNX. Jan 18, 2017 Download for free at http://cnx.org/content/col12116/1.2
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