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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

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

0.000066

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

0.2397

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

0.0000

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

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

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.

1,000,000 times 2.57 equals 2570000. An arrows shows  how the decimal in 2.57 is moved six digits to the right to make 2,570,000.

1,000 times 0.0000029 equals 0.0029. An arrows shows  how the decimal in 0.0000029 is moved six digits to the right to make 0.0029.

Practice set c

Find the following products.

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

427

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

165,218.7

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

0.188

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

527,000,000,000

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.

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.

Practice set d

Find 2.8 of 6.4.

17.92

Find 0.1 of 1.3.

0.13

Find 1.01 of 3.6.

3.636

Find 0.004 of 0.0009.

0.0000036

Find 0.83 of 12.

9.96

Find 1.1 of the sum of 8.6 and 4.2.

14.08

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

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

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

47.20

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

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

0.152

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

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

4.6324

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

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

3.182

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

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

0.0000273

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

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

2.56

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

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

0.81

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

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

29.3045

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

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

0.00000105486

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

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

49.6

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

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

4,218.842

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

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

19.621

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

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

3,596.168

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

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

25,010

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

( 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

( 8 . 09 ) ( 7 . 1 ) size 12{ \( 8 "." "09" \) \( 7 "." 1 \) } {}

Actual product Tenths Hundreds Thousandths

( 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

0 . 0083 1 . 090901 size 12{0 "." "0083" cdot 1 "." "090901"} {}

Actual product Tenths Hundreds Thousandths

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

For the following 15 problems, perform the indicated operations

Find 5.2 of 3.7.

Find 12.03 of 10.1

121.503

Find 16 of 1.04

Find 12 of 0.1

1.2

Find 0.09 of 0.003

Find 1.02 of 0.9801

0.999702

Find 0.01 of the sum of 3.6 and 12.18

Find 0.2 of the sum of 0.194 and 1.07

0.2528

Find the difference of 6.1 of 2.7 and 2.7 of 4.03

Find the difference of 0.071 of 42 and 0.003 of 9.2

2.9544

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

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

$16.24

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

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

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?

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

0.261 1.96

4.826 4.827

23.295102

9.46 2

0.012 2

0.000144

0.00037 0.0065

0.002 0.0009

0.0000018

0.1286 0.7699

0.01 0.00000471

0.0000000471

0.00198709 0.03

Exercises for review

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

0

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

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

10 77

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

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

1.78

Questions & Answers

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 to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
China
Cied
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Contemporary math applications. OpenStax CNX. Dec 15, 2014 Download for free at http://legacy.cnx.org/content/col11559/1.6
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