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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

what is variations in raman spectra for nanomaterials
Jyoti Reply
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
Daniel
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
Privacy Information Security Software Version 1.1a
Good
7hours 36 min - 4hours 50 min
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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