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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

how does Neisseria cause meningitis
Nyibol Reply
what is microbiologist
Muhammad Reply
what is errata
Muhammad
is the branch of biology that deals with the study of microorganisms.
Ntefuni Reply
What is microbiology
Mercy Reply
studies of microbes
Louisiaste
when we takee the specimen which lumbar,spin,
Ziyad Reply
How bacteria create energy to survive?
Muhamad Reply
Bacteria doesn't produce energy they are dependent upon their substrate in case of lack of nutrients they are able to make spores which helps them to sustain in harsh environments
_Adnan
But not all bacteria make spores, l mean Eukaryotic cells have Mitochondria which acts as powerhouse for them, since bacteria don't have it, what is the substitution for it?
Muhamad
they make spores
Louisiaste
what is sporadic nd endemic, epidemic
Aminu Reply
the significance of food webs for disease transmission
Abreham
food webs brings about an infection as an individual depends on number of diseased foods or carriers dully.
Mark
explain assimilatory nitrate reduction
Esinniobiwa Reply
Assimilatory nitrate reduction is a process that occurs in some microorganisms, such as bacteria and archaea, in which nitrate (NO3-) is reduced to nitrite (NO2-), and then further reduced to ammonia (NH3).
Elkana
This process is called assimilatory nitrate reduction because the nitrogen that is produced is incorporated in the cells of microorganisms where it can be used in the synthesis of amino acids and other nitrogen products
Elkana
Examples of thermophilic organisms
Shu Reply
Give Examples of thermophilic organisms
Shu
advantages of normal Flora to the host
Micheal Reply
Prevent foreign microbes to the host
Abubakar
they provide healthier benefits to their hosts
ayesha
They are friends to host only when Host immune system is strong and become enemies when the host immune system is weakened . very bad relationship!
Mark
what is cell
faisal Reply
cell is the smallest unit of life
Fauziya
cell is the smallest unit of life
Akanni
ok
Innocent
cell is the structural and functional unit of life
Hasan
is the fundamental units of Life
Musa
what are emergency diseases
Micheal Reply
There are nothing like emergency disease but there are some common medical emergency which can occur simultaneously like Bleeding,heart attack,Breathing difficulties,severe pain heart stock.Hope you will get my point .Have a nice day ❣️
_Adnan
define infection ,prevention and control
Innocent
I think infection prevention and control is the avoidance of all things we do that gives out break of infections and promotion of health practices that promote life
Lubega
Heyy Lubega hussein where are u from?
_Adnan
en français
Adama
which site have a normal flora
ESTHER Reply
Many sites of the body have it Skin Nasal cavity Oral cavity Gastro intestinal tract
Safaa
skin
Asiina
skin,Oral,Nasal,GIt
Sadik
How can Commensal can Bacteria change into pathogen?
Sadik
How can Commensal Bacteria change into pathogen?
Sadik
all
Tesfaye
by fussion
Asiina
what are the advantages of normal Flora to the host
Micheal
what are the ways of control and prevention of nosocomial infection in the hospital
Micheal
what is inflammation
Shelly Reply
part of a tissue or an organ being wounded or bruised.
Wilfred
what term is used to name and classify microorganisms?
Micheal Reply
Binomial nomenclature
adeolu
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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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