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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.

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

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

0.005

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

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.

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.

Practice set d

Find the decimal representation of each quotient.

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

18.25

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

1.825

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

0.1825

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

0.01825

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

6.4618

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

0.021926

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

16 . 8 ÷ 8 size 12{"16" "." 8÷8} {}

18 . 5 ÷ 5 size 12{"18" "." 5÷5} {}

3.7

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

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

6.04

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

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

9.38

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

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

0.46

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

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

8.6

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

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

2.4

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

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

6.21

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

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

2.18

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

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

1.001

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

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

4

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

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

14

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

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

111

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

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

643.51006

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

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

0.064351006

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

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

45 . 32931 ÷ 9 . 01 size 12{"45" "." "32931"÷9 "." "01"} {}

Actual Quotient Tenths Hundredths Thousandths

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

4 . 3636 ÷ 4 size 12{4 "." "3636"÷4} {}

Actual Quotient Tenths Hundredths Thousandths

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

For the following 9 problems, find each solution.

Divide the product of 7.4 and 4.1 by 2.6.

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

0.01

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.

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

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

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

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?

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

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?

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

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

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

29.120

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

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

0.173

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

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

1.111

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

Exercises for review

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

39 8

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

( [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

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

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

2.8634

Questions & Answers

Do somebody tell me a best nano engineering book for beginners?
s. Reply
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
s.
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
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
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
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
AMJAD
preparation of nanomaterial
Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
good afternoon madam
AMJAD
what is system testing
AMJAD
what is the application of nanotechnology?
Stotaw
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
Hello
Uday
I'm interested in Nanotube
Uday
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
Prasenjit
can nanotechnology change the direction of the face of the world
Prasenjit Reply
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
Ali Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
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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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