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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

A golfer on a fairway is 70 m away from the green, which sits below the level of the fairway by 20 m. If the golfer hits the ball at an angle of 40° with an initial speed of 20 m/s, how close to the green does she come?
Aislinn Reply
cm
tijani
what is titration
John Reply
what is physics
Siyaka Reply
A mouse of mass 200 g falls 100 m down a vertical mine shaft and lands at the bottom with a speed of 8.0 m/s. During its fall, how much work is done on the mouse by air resistance
Jude Reply
Can you compute that for me. Ty
Jude
what is the dimension formula of energy?
David Reply
what is viscosity?
David
what is inorganic
emma Reply
what is chemistry
Youesf Reply
what is inorganic
emma
Chemistry is a branch of science that deals with the study of matter,it composition,it structure and the changes it undergoes
Adjei
please, I'm a physics student and I need help in physics
Adjanou
chemistry could also be understood like the sexual attraction/repulsion of the male and female elements. the reaction varies depending on the energy differences of each given gender. + masculine -female.
Pedro
A ball is thrown straight up.it passes a 2.0m high window 7.50 m off the ground on it path up and takes 1.30 s to go past the window.what was the ball initial velocity
Krampah Reply
2. A sled plus passenger with total mass 50 kg is pulled 20 m across the snow (0.20) at constant velocity by a force directed 25° above the horizontal. Calculate (a) the work of the applied force, (b) the work of friction, and (c) the total work.
Sahid Reply
you have been hired as an espert witness in a court case involving an automobile accident. the accident involved car A of mass 1500kg which crashed into stationary car B of mass 1100kg. the driver of car A applied his brakes 15 m before he skidded and crashed into car B. after the collision, car A s
Samuel Reply
can someone explain to me, an ignorant high school student, why the trend of the graph doesn't follow the fact that the higher frequency a sound wave is, the more power it is, hence, making me think the phons output would follow this general trend?
Joseph Reply
Nevermind i just realied that the graph is the phons output for a person with normal hearing and not just the phons output of the sound waves power, I should read the entire thing next time
Joseph
Follow up question, does anyone know where I can find a graph that accuretly depicts the actual relative "power" output of sound over its frequency instead of just humans hearing
Joseph
"Generation of electrical energy from sound energy | IEEE Conference Publication | IEEE Xplore" ***ieeexplore.ieee.org/document/7150687?reload=true
Ryan
what's motion
Maurice Reply
what are the types of wave
Maurice
answer
Magreth
progressive wave
Magreth
hello friend how are you
Muhammad Reply
fine, how about you?
Mohammed
hi
Mujahid
A string is 3.00 m long with a mass of 5.00 g. The string is held taut with a tension of 500.00 N applied to the string. A pulse is sent down the string. How long does it take the pulse to travel the 3.00 m of the string?
yasuo Reply
Who can show me the full solution in this problem?
Reofrir 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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