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Practice set b

Use a calculator to find each product. If the calculator will not provide the exact product, round the result to four decimal places.

5 . 126 4 . 08 size 12{5 "." "126 " cdot " 4" "." "08"} {}

20.91408

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0 . 00165 0 . 04 size 12{0 "." "00165 " cdot " 0" "." "04"} {}

0.000066

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0 . 5598 0 . 4281 size 12{0 "." "5598 " cdot " 0" "." "4281"} {}

0.2397

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0 . 000002 0 . 06 size 12{0 "." "000002 " cdot " 0" "." "06"} {}

0.0000

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Multiplying decimals by powers of 10

There is an interesting feature of multiplying decimals by powers of 10. Consider the following multiplications.

Multiplication Number of Zeros in the Power of 10 Number of Positions the Decimal Point Has Been Moved to the Right
10 8 . 315274 = 83 . 15274 size 12{"10" cdot 8 "." "315274"="83" "." "15274"} {} 1 1
100 8 . 315274 = 831 . 5274 size 12{"100" cdot 8 "." "315274"="831" "." "5274"} {} 2 2
1, 000 8 . 315274 = 8, 315 . 274 size 12{1,"000" cdot 8 "." "315274"=8,"315" "." "274"} {} 3 3
10 , 000 8 . 315274 = 83 , 152 . 74 size 12{"10","000" cdot 8 "." "315274"="83","152" "." "74"} {} 4 4

Multiplying a decimal by a power of 10

To multiply a decimal by a power of 10, move the decimal place to the right of its current position as many places as there are zeros in the power of 10. Add zeros if necessary.

Sample set c

Find the following products.

100 34 . 876 size 12{"100" cdot "34" "." "876"} {} . Since there are 2 zeros in 100, Move the decimal point in 34.876 two places to the right.

100 times 34.876 equals 3487.6. An arrows shows  how the decimal in 34.876 is moved two digits to the right to make 3,487.6

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1, 000 4 . 8058 size 12{1,"000" cdot 4 "." "8058"} {} . Since there are 3 zeros in 1,000, move the decimal point in 4.8058 three places to the right.

1,000 times 4.8058 equals 4805.8. An arrows shows  how the decimal in 4.8058 is moved three digits to the right to make 4,805.8

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10 , 000 56 . 82 size 12{"10","000" cdot "56" "." "82"} {} . Since there are 4 zeros in 10,000, move the decimal point in 56.82 four places to the right. We will have to add two zeros in order to obtain the four places.

10,000 times 56.82 equals 568200. An arrows shows  how the decimal in 56.82 is moved four digits to the right to make 568,200.
Since there is no fractional part, we can drop the decimal point.

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Practice set c

Find the following products.

100 4 . 27 size 12{"100 " cdot " 4" "." "27"} {}

427

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10,000 16 . 52187 size 12{"10,000 " cdot " 16" "." "52187"} {}

165,218.7

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( 10 ) ( 0 . 0188 ) size 12{ \( "10" \) \( 0 "." "0188" \) } {}

0.188

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( 10,000,000,000 ) ( 52 . 7 ) size 12{ \( "10,000,000,000" \) \( "52" "." 7 \) } {}

527,000,000,000

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Multiplication in terms of “of”

Recalling that the word "of" translates to the arithmetic operation of multiplica­tion, let's observe the following multiplications.

Sample set d

Find 4.1 of 3.8.

Translating "of" to "×", we get

4.1 × 3.8 ̲ 328 123    ̲ 15.58

Thus, 4.1 of 3.8 is 15.58.

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Find 0.95 of the sum of 2.6 and 0.8.

We first find the sum of 2.6 and 0.8.

2.6 + 0.8 ̲ 3.4

Now find 0.95 of 3.4

3.4 × 0.95 ̲ 170 306    ̲ 3.230

Thus, 0.95 of ( 2 . 6 + 0 . 8 ) size 12{ \( 2 "." "6 "+" 0" "." 8 \) } {} is 3.230.

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Practice set d

Find 0.004 of 0.0009.

0.0000036

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Find 1.1 of the sum of 8.6 and 4.2.

14.08

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Exercises

For the following 30 problems, find each product and check each result with a calculator.

3 . 4 9 . 2 size 12{3 "." 4 cdot 9 "." 2} {}

31.28

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4 . 5 6 . 1 size 12{4 "." 5 cdot 6 "." 1} {}

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8 . 0 5 . 9 size 12{8 "." 0 cdot 5 "." 9} {}

47.20

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6 . 1 7 size 12{6 "." 1 cdot 7} {}

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( 0 . 1 ) ( 1 . 52 ) size 12{ \( 0 "." 1 \) \( 1 "." "52" \) } {}

0.152

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( 1 . 99 ) ( 0 . 05 ) size 12{ \( 1 "." "99" \) \( 0 "." "05" \) } {}

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( 12 . 52 ) ( 0 . 37 ) size 12{ \( "12" "." "52" \) \( 0 "." "37" \) } {}

4.6324

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( 5 . 116 ) ( 1 . 21 ) size 12{ \( 5 "." "116" \) \( 1 "." "21" \) } {}

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( 31 . 82 ) ( 0 . 1 ) size 12{ \( "31" "." "82" \) \( 0 "." 1 \) } {}

3.182

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( 16 . 527 ) ( 9 . 16 ) size 12{ \( "16" "." "527" \) \( 9 "." "16" \) } {}

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0 . 0021 0 . 013 size 12{0 "." "0021" cdot 0 "." "013"} {}

0.0000273

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1 . 0037 1 . 00037 size 12{1 "." "0037" cdot 1 "." "00037"} {}

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( 1 . 6 ) ( 1 . 6 ) size 12{ \( 1 "." 6 \) \( 1 "." 6 \) } {}

2.56

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( 4 . 2 ) ( 4 . 2 ) size 12{ \( 4 "." 2 \) \( 4 "." 2 \) } {}

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0 . 9 0 . 9 size 12{0 "." 9 cdot 0 "." 9} {}

0.81

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1 . 11 1 . 11 size 12{1 "." "11" cdot 1 "." "11"} {}

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6 . 815 4 . 3 size 12{6 "." "815" cdot 4 "." 3} {}

29.3045

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9 . 0168 1 . 2 size 12{9 "." "0168" cdot 1 "." 2} {}

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( 3 . 5162 ) ( 0 . 0000003 ) size 12{ \( 3 "." "5162" \) \( 0 "." "0000003" \) } {}

0.00000105486

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( 0 . 000001 ) ( 0 . 01 ) size 12{ \( 0 "." "000001" \) \( 0 "." "01" \) } {}

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( 10 ) ( 4 . 96 ) size 12{ \( "10" \) \( 4 "." "96" \) } {}

49.6

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( 10 ) ( 36 . 17 ) size 12{ \( "10" \) \( "36" "." "17" \) } {}

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10 421 . 8842 size 12{"10" cdot "421" "." "8842"} {}

4,218.842

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10 8 . 0107 size 12{"10" cdot 8 "." "0107"} {}

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100 0 . 19621 size 12{"100" cdot 0 "." "19621"} {}

19.621

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100 0 . 779 size 12{"100" cdot 0 "." "779"} {}

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1000 3 . 596168 size 12{"1000" cdot 3 "." "596168"} {}

3,596.168

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1000 42 . 7125571 size 12{"1000" cdot "42" "." "7125571"} {}

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1000 25 . 01 size 12{"1000" cdot "25" "." "01"} {}

25,010

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100 , 000 9 . 923 size 12{"100","000" cdot 9 "." "923"} {}

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( 4 . 6 ) ( 6 . 17 ) size 12{ \( 4 "." 6 \) \( 6 "." "17" \) } {}

Actual product Tenths Hundreds Thousandths
Actual product Tenths Hundreds Thousandths
28.382 28.4 28.38 28.382
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( 8 . 09 ) ( 7 . 1 ) size 12{ \( 8 "." "09" \) \( 7 "." 1 \) } {}

Actual product Tenths Hundreds Thousandths
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( 11 . 1106 ) ( 12 . 08 ) size 12{ \( "11" "." "1106" \) \( "12" "." "08" \) } {}

Actual product Tenths Hundreds Thousandths
Actual product Tenths Hundreds Thousandths
134.216048 134.2 134.22 134.216
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0 . 0083 1 . 090901 size 12{0 "." "0083" cdot 1 "." "090901"} {}

Actual product Tenths Hundreds Thousandths
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7 26 . 518 size 12{7 cdot "26" "." "518"} {}

Actual product Tenths Hundreds Thousandths
Actual product Tenths Hundreds Thousandths
185.626 185.6 185.63 185.626
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For the following 15 problems, perform the indicated operations

Find 12.03 of 10.1

121.503

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Find 1.02 of 0.9801

0.999702

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Find 0.01 of the sum of 3.6 and 12.18

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Find 0.2 of the sum of 0.194 and 1.07

0.2528

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Find the difference of 6.1 of 2.7 and 2.7 of 4.03

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Find the difference of 0.071 of 42 and 0.003 of 9.2

2.9544

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If a person earns $8.55 an hour, how much does he earn in twenty-five hundredths of an hour?

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A man buys 14 items at $1.16 each. What is the total cost?

$16.24

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In the problem above, how much is the total cost if 0.065 sales tax is added?

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A river rafting trip is supposed to last for 10 days and each day 6 miles is to be rafted. On the third day a person falls out of the raft after only 2 5 size 12{ { {2} over {5} } } {} of that day’s mileage. If this person gets discouraged and quits, what fraction of the entire trip did he complete?

0.24

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A woman starts the day with $42.28. She buys one item for $8.95 and another for $6.68. She then buys another item for sixty two-hundredths of the remaining amount. How much money does she have left?

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Calculator problems

For the following 10 problems, use a calculator to determine each product. If the calculator will not provide the exact product, round the results to five decimal places.

0.019 0.321

0.006099

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4.826 4.827

23.295102

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0.002 0.0009

0.0000018

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0.01 0.00000471

0.0000000471

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Exercises for review

( [link] ) Find the value, if it exists, of 0 ÷ 15 size 12{"0 " div " 15"} {} .

0

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( [link] ) Find the greatest common factor of 210, 231, and 357.

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( [link] ) Reduce 280 2, 156 size 12{ { {"280"} over {2,"156"} } } {} to lowest terms.

10 77

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( [link] ) Write "fourteen and one hundred twenty-one ten-thousandths, using digits."

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( [link] ) Subtract 6.882 from 8.661 and round the result to two decimal places.

1.78

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Questions & Answers

can someone help me with some logarithmic and exponential equations.
Jeffrey Reply
sure. what is your question?
ninjadapaul
20/(×-6^2)
Salomon
okay, so you have 6 raised to the power of 2. what is that part of your answer
ninjadapaul
I don't understand what the A with approx sign and the boxed x mean
ninjadapaul
it think it's written 20/(X-6)^2 so it's 20 divided by X-6 squared
Salomon
I'm not sure why it wrote it the other way
Salomon
I got X =-6
Salomon
ok. so take the square root of both sides, now you have plus or minus the square root of 20= x-6
ninjadapaul
oops. ignore that.
ninjadapaul
so you not have an equal sign anywhere in the original equation?
ninjadapaul
Commplementary angles
Idrissa Reply
hello
Sherica
im all ears I need to learn
Sherica
right! what he said ⤴⤴⤴
Tamia
what is a good calculator for all algebra; would a Casio fx 260 work with all algebra equations? please name the cheapest, thanks.
Kevin Reply
a perfect square v²+2v+_
Dearan Reply
kkk nice
Abdirahman Reply
algebra 2 Inequalities:If equation 2 = 0 it is an open set?
Kim Reply
or infinite solutions?
Kim
The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
Al
y=10×
Embra Reply
if |A| not equal to 0 and order of A is n prove that adj (adj A = |A|
Nancy Reply
rolling four fair dice and getting an even number an all four dice
ramon Reply
Kristine 2*2*2=8
Bridget Reply
Differences Between Laspeyres and Paasche Indices
Emedobi Reply
No. 7x -4y is simplified from 4x + (3y + 3x) -7y
Mary Reply
is it 3×y ?
Joan Reply
J, combine like terms 7x-4y
Bridget Reply
im not good at math so would this help me
Rachael Reply
yes
Asali
I'm not good at math so would you help me
Samantha
what is the problem that i will help you to self with?
Asali
how do you translate this in Algebraic Expressions
linda Reply
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
Crystal Reply
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
Chris Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
China
Cied
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
AMJAD
preparation of nanomaterial
Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
good afternoon madam
AMJAD
what is system testing
AMJAD
what is the application of nanotechnology?
Stotaw
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
can nanotechnology change the direction of the face of the world
Prasenjit Reply
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
Ali Reply
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
bamidele Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Tanis Reply

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Source:  OpenStax, Fundamentals of mathematics. OpenStax CNX. Aug 18, 2010 Download for free at http://cnx.org/content/col10615/1.4
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