<< Chapter < Page Chapter >> Page >

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.

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

0.005

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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.

Got questions? Get instant answers now!

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.

Got questions? Get instant answers now!

Practice set d

Find the decimal representation of each quotient.

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

18.25

Got questions? Get instant answers now!

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

1.825

Got questions? Get instant answers now!

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

0.1825

Got questions? Get instant answers now!

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

0.01825

Got questions? Get instant answers now!

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

6.4618

Got questions? Get instant answers now!

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

0.021926

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

16 . 8 ÷ 8 size 12{"16" "." 8÷8} {}

Got questions? Get instant answers now!

18 . 5 ÷ 5 size 12{"18" "." 5÷5} {}

3.7

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

6.04

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

9.38

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

0.46

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

8.6

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

2.4

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

6.21

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

2.18

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

1.001

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

4

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

14

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

111

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

643.51006

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

0.064351006

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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
Got questions? Get instant answers now!

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

Actual Quotient Tenths Hundredths Thousandths
Got questions? Get instant answers now!

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
Got questions? Get instant answers now!

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

Actual Quotient Tenths Hundredths Thousandths
Got questions? Get instant answers now!

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
Got questions? Get instant answers now!

For the following 9 problems, find each solution.

Divide the product of 7.4 and 4.1 by 2.6.

Got questions? Get instant answers now!

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

0.01

Got questions? Get instant answers now!

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.

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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?

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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?

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

29.120

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

0.173

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

1.111

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

Exercises for review

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

39 8

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

( [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

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

2.8634

Got questions? Get instant answers now!

Questions & Answers

discuss how the following factors such as predation risk, competition and habitat structure influence animal's foraging behavior in essay form
Burnet Reply
location of cervical vertebra
KENNEDY Reply
What are acid
Sheriff Reply
define biology infour way
Happiness Reply
What are types of cell
Nansoh Reply
how can I get this book
Gatyin Reply
what is lump
Chineye Reply
what is cell
Maluak Reply
what is biology
Maluak
what's cornea?
Majak Reply
what are cell
Achol
Explain the following terms . (1) Abiotic factors in an ecosystem
Nomai Reply
Abiotic factors are non living components of ecosystem.These include physical and chemical elements like temperature,light,water,soil,air quality and oxygen etc
Qasim
Define the term Abiotic
Marial
what is biology
daniel Reply
what is diffusion
Emmanuel Reply
passive process of transport of low-molecular weight material according to its concentration gradient
AI-Robot
what is production?
Catherine
hello
Marial
Pathogens and diseases
how did the oxygen help a human being
Achol Reply
how did the nutrition help the plants
Achol Reply
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, Fundamentals of mathematics. OpenStax CNX. Aug 18, 2010 Download for free at http://cnx.org/content/col10615/1.4
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Fundamentals of mathematics' conversation and receive update notifications?

Ask