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0 . 8215199 ÷ 4 . 113 size 12{0 "." "8215199" div 4 "." "113"} {}

Display Reads
Type .8215199 0.8215199
Press ÷ 0.8215199
Type 4.113 4.113
Press = 0.1997373

There are EIGHT DIGITS — DISPLAY FILLED! BE AWARE OF POSSIBLE APPROXI­MATIONS.

We can check for a possible approximation in the following way. Since the division 4 12 3 can be checked by multiplying 4 and 3, we can check our division by performing the multiplication

4.113 3 decimal places × 0.1997373 7 decimal places

This multiplication produces 3 + 7 = 10 size 12{3+7="10"} {} decimal digits. But our suspected quotient contains only 8 decimal digits. We conclude that the answer is an approximation. Then, rounding to five decimal places, we get 0.19974.

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Practice set c

Find each quotient using a calculator. If the result is an approximation, round to four decimal places.

42 . 49778 ÷ 14 . 261 size 12{"42" "." "49778" div "14" "." "261"} {}

2.98

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0 . 001455 ÷ 0 . 291 size 12{0 "." "001455" div 0 "." "291"} {}

0.005

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7 . 459085 ÷ 2 . 1192 size 12{7 "." "459085" div 2 "." "1192"} {}

3.5197645 is an approximate result. Rounding to four decimal places, we get 3.5198

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Dividing decimals by powers of 10

In problems 4 and 5 of [link] , we found the decimal representations of 8, 162 . 41 ÷ 10 size 12{8,"162" "." "41" div "10"} {} and 8, 162 . 41 ÷ 100 size 12{8,"162" "." "41" div "100"} {} . Let's look at each of these again and then, from these observations, make a general statement regarding division of a decimal num­ber by a power of 10.

816.241 10 8162.410 80            ̲ 16          10          ̲ 62        60        ̲ 24      20      ̲ 41    40    ̲ 10  10  ̲

Thus, 8, 162 . 41 ÷ 10 = 816 . 241 size 12{8,"162" "." "41" div "10"="816" "." "241"} {} .

Notice that the divisor 10 is composed of one 0 and that the quotient 816.241 can be obtained from the dividend 8,162.41 by moving the decimal point one place to the left.

81.6241 100 8162.4100 800            ̲ 162          100          ̲ 62 4       60 0       ̲ 2 41     2 00     ̲ 410   400   ̲ 100 100 ̲ 0

Thus, 8, 162 . 41 ÷ 100 = 81 . 6241 size 12{8,"162" "." "41" div "100"="81" "." "6241"} {} .

Notice that the divisor 100 is composed of two 0's and that the quotient 81.6241 can be obtained from the dividend by moving the decimal point two places to the left.

Using these observations, we can suggest the following method for dividing decimal numbers by powers of 10.

Dividing a decimal fraction by a power of 10

To divide a decimal fraction by a power of 10, move the decimal point of the decimal fraction to the left as many places as there are zeros in the power of 10. Add zeros if necessary.

Sample set d

Find each quotient.

9, 248 . 6 ÷ 100 size 12{9,"248" "." 6 div "100"} {}
Since there are 2 zeros in this power of 10, we move the decimal point 2 places to the left.

9248.6 divided by 100 is equal to 92.480. Notice that the only effect is the movement of a decimal two places to the left of 9248.6.

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3 . 28 ÷ 10 , 000 size 12{3 "." "28" div "10","000"} {}

Since there are 4 zeros in this power of 10, we move the decimal point 4 places to the left. To do so, we need to add three zeros.

3.28 divided by 10,000 is equal to 0.000328. Notice that the only effect is the movement of a decimal four places to the left of 0003.28.

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Practice set d

Find the decimal representation of each quotient.

182 . 5 ÷ 10 size 12{"182" "." 5 div "10"} {}

18.25

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182 . 5 ÷ 100 size 12{"182" "." 5 div "100"} {}

1.825

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182 . 5 ÷ 1, 000 size 12{"182" "." 5 div 1,"000"} {}

0.1825

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182 . 5 ÷ 10 , 000 size 12{"182" "." 5 div "10","000"} {}

0.01825

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646 . 18 ÷ 100 size 12{"646" "." "18" div "100"} {}

6.4618

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21 . 926 ÷ 1, 000 size 12{"21" "." "926" div 1,"000"} {}

0.021926

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Exercises

For the following 30 problems, find the decimal representation of each quotient. Use a calculator to check each result.

4 . 8 ÷ 3 size 12{4 "." 8÷3} {}

1.6

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16 . 8 ÷ 8 size 12{"16" "." 8÷8} {}

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18 . 5 ÷ 5 size 12{"18" "." 5÷5} {}

3.7

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12 . 33 ÷ 3 size 12{"12" "." "33"÷3} {}

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54 . 36 ÷ 9 size 12{"54" "." "36"÷9} {}

6.04

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73 . 56 ÷ 12 size 12{"73" "." "56"÷"12"} {}

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159 . 46 ÷ 17 size 12{"159" "." "46"÷"17"} {}

9.38

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12 . 16 ÷ 64 size 12{"12" "." "16"÷"64"} {}

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37 . 26 ÷ 81 size 12{"37" "." "26"÷"81"} {}

0.46

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439 . 35 ÷ 435 size 12{"439" "." "35"÷"435"} {}

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36 . 98 ÷ 4 . 3 size 12{"36" "." "98"÷4 "." 3} {}

8.6

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46 . 41 ÷ 9 . 1 size 12{"46" "." "41"÷9 "." 1} {}

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3 . 6 ÷ 1 . 5 size 12{3 "." 6÷1 "." 5} {}

2.4

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0 . 68 ÷ 1 . 7 size 12{0 "." "68"÷1 "." 7} {}

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50 . 301 ÷ 8 . 1 size 12{"50" "." "301"÷8 "." 1} {}

6.21

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2 . 832 ÷ 0 . 4 size 12{2 "." "832"÷0 "." 4} {}

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4 . 7524 ÷ 2 . 18 size 12{4 "." "7524"÷2 "." "18"} {}

2.18

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16 . 2409 ÷ 4 . 03 size 12{"16" "." "2409"÷4 "." "03"} {}

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1 . 002001 ÷ 1 . 001 size 12{1 "." "002001"÷1 "." "001"} {}

1.001

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25 . 050025 ÷ 5 . 005 size 12{"25" "." "050025"÷5 "." "005"} {}

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12 . 4 ÷ 3 . 1 size 12{"12" "." 4÷3 "." 1} {}

4

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0 . 48 ÷ 0 . 08 size 12{0 "." "48"÷0 "." "08"} {}

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30 . 24 ÷ 2 . 16 size 12{"30" "." "24"÷2 "." "16"} {}

14

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48 . 87 ÷ 0 . 87 size 12{"48" "." "87"÷0 "." "87"} {}

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12 . 321 ÷ 0 . 111 size 12{"12" "." "321"÷0 "." "111"} {}

111

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64 , 351 . 006 ÷ 10 size 12{"64","351" "." "006"÷"10"} {}

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64 , 351 . 006 ÷ 100 size 12{"64","351" "." "006"÷"100"} {}

643.51006

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64 , 351 . 006 ÷ 1, 000 size 12{"64","351" "." "006"÷1,"000"} {}

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64 , 351 . 006 ÷ 1, 000 , 000 size 12{"64","351" "." "006"÷1,"000","000"} {}

0.064351006

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0 . 43 ÷ 100 size 12{0 "." "43"÷"100"} {}

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For the following 5 problems, find each quotient. Round to the specified position. A calculator may be used.

11 . 2944 ÷ 6 . 24 size 12{"11" "." "2944"÷6 "." "24"} {}

Actual Quotient Tenths Hundredths Thousandths
Actual Quotient Tenths Hundredths Thousandths
1.81 1.8 1.81 1.810
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45 . 32931 ÷ 9 . 01 size 12{"45" "." "32931"÷9 "." "01"} {}

Actual Quotient Tenths Hundredths Thousandths
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3 . 18186 ÷ 0 . 66 size 12{3 "." "18186"÷0 "." "66"} {}

Actual Quotient Tenths Hundredths Thousandths
Actual Quotient Tenths Hundredths Thousandths
4.821 4.8 4.82 4.821
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4 . 3636 ÷ 4 size 12{4 "." "3636"÷4} {}

Actual Quotient Tenths Hundredths Thousandths
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0 . 00006318 ÷ 0 . 018 size 12{0 "." "00006318"÷0 "." "018"} {}

Actual Quotient Tenths Hundredths Thousandths
Actual Quotient Tenths Hundredths Thousandths
0.00351 0.0 0.00 0.004
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For the following 9 problems, find each solution.

Divide the product of 7.4 and 4.1 by 2.6.

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Divide the product of 11.01 and 0.003 by 2.56 and round to two decimal places.

0.01

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Divide the difference of the products of 2.1 and 9.3, and 4.6 and 0.8 by 0.07 and round to one decimal place.

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A ring costing $567.08 is to be paid off in equal monthly payments of $46.84. In how many months will the ring be paid off?

12.11 months

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Six cans of cola cost $2.58. What is the price of one can?

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A family traveled 538.56 miles in their car in one day on their vacation. If their car used 19.8 gallons of gas, how many miles per gallon did it get?

27.2 miles per gallon

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Three college students decide to rent an apartment together. The rent is $812.50 per month. How much must each person contribute toward the rent?

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A woman notices that on slow speed her video cassette recorder runs through 296.80 tape units in 10 minutes and at fast speed through 1098.16 tape units. How many times faster is fast speed than slow speed?

3.7

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A class of 34 first semester business law students pay a total of $1,354.90, disregarding sales tax, for their law textbooks. What is the cost of each book?

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Calculator problems

For the following problems, use calculator to find the quotients. If the result is approximate (see Sample Set C [link] ) round the result to three decimal places.

3 . 8994 ÷ 2 . 01 size 12{3 "." "8994"÷2 "." "01"} {}

1.94

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0 . 067444 ÷ 0 . 052 size 12{0 "." "067444"÷0 "." "052"} {}

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14 , 115 . 628 ÷ 484 . 74 size 12{"14","115" "." "628"÷"484" "." "74"} {}

29.120

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219 , 709 . 36 ÷ 9941 . 6 size 12{"219","709" "." "36"÷"9941" "." 6} {}

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0 . 0852092 ÷ 0 . 49271 size 12{0 "." "0852092"÷0 "." "49271"} {}

0.173

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2 . 4858225 ÷ 1 . 11611 size 12{2 "." "4858225"÷1 "." "11611"} {}

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0 . 123432 ÷ 0 . 1111 size 12{0 "." "123432"÷0 "." "1111"} {}

1.111

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2 . 102838 ÷ 1 . 0305 size 12{2 "." "102838"÷1 "." "0305"} {}

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Exercises for review

( [link] ) Convert 4 7 8 size 12{4 { {7} over {8} } } {} to an improper fraction.

39 8

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( [link] ) 2 7 size 12{ { {2} over {7} } } {} of what number is 4 5 size 12{ { {4} over {5} } } {} ?

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( [link] ) Find the sum. 4 15 + 7 10 + 3 5 size 12{ { {4} over {"15"} } + { {7} over {"10"} } + { {3} over {5} } } {} .

47 30 or 1 17 30

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( [link] ) Round 0.01628 to the nearest ten-thousandths.

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( [link] ) Find the product (2.06)(1.39)

2.8634

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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
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what is titration
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what is physics
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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
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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.
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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
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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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