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Sample set c

Estimate the product: 73 46 size 12{"73 " cdot " 46"} {} .

Notice that 73 is near 70, one nonzero digit and that 46 is near 50. one nonzero digit

The product can be estimated by 70 50 = 3,500 size 12{"70 " cdot " 50 "=" 3,500"} {} . (Recall that to multiply numbers ending in zeros, we multiply the nonzero digits and affix to this product the total number of ending zeros in the factors. See [link] for a review of this technique.)

Thus, 73 46 size 12{"73 " cdot " 46"} {} is about 3,500. In fact, 73 46 = 3,358 size 12{"73 " cdot " 46 "=" 3,358"} {} .

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Estimate the product: 87 4,316 size 12{"87 " cdot " 4,316"} {} .

Notice that 87 is close to 90, one nonzero digit and that 4,316 is close to 4,000. one nonzero digit

The product can be estimated by 90 4,000 = 360,000 size 12{"90 " cdot " 4,000 "=" 360,000"} {} .

Thus, 87 4,316 size 12{"87 " cdot " 4,316"} {} is about 360,000. In fact, 87 4,316 = 375,492 size 12{"87 " cdot " 4,316 "=" 375,492"} {} .

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Practice set c

Estimate the product: 31 87 size 12{"31 " cdot " 87"} {} .

31 87 : 30 90 . About 2,700. In fact, 2,697.

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Estimate the product: 18 42 size 12{"18 " cdot " 42"} {} .

18 42 : 20 40 . About 800. In fact, 756.

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Estimate the product: 16 94 size 12{"16 " cdot " 94"} {} .

16 94 : 15 100 . About 1,500. In fact, 1,504.

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Sample set d

Estimate the quotient: 153 ÷ 17 size 12{"153 " div " 17"} {} .

Notice that 153 is close to 150, two nonzero digits and that 17 is close to 15. two nonzero digits

The quotient can be estimated by 150 ÷ 15 = 10 size 12{"150 " div " 15 "=" 10"} {} .

Thus, 153 ÷ 17 size 12{"153 " div " 17"} {} is about 10. In fact, 153 ÷ 17 = 9 size 12{"153 " div " 17 "=" 9"} {} .

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Estimate the quotient: 742,000 ÷ 2,400 size 12{"742,000 " div " 2,400"} {} .

Notice that 742,000 is close to 700,000 one nonzero digit , and that 2,400 is close to 2,000. one nonzero digit

The quotient can be estimated by 700,000 ÷ 2,000 = 350 size 12{"700,000 " div " 2,000 "=" 350"} {} .

Thus, 742,000 ÷ 2,400 size 12{"742,000 " div " 2,400"} {} is about 350. In fact, 742,000 ÷ 2,400 = 309 . 1 6 ¯ size 12{"742,000 " div " 2,400 "=" 309" "." 1 {overline {6}} } {} .

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Practice set d

Estimate the quotient: 221 ÷ 18 size 12{"221 " div " 18"} {} .

221 ÷ 18 : 200 ÷ 20 . About 10. In fact, 12.27.

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Estimate the quotient: 4,079 ÷ 381 size 12{"4,079 " div " 381"} {} .

4,079 ÷ 381 : 4,000 ÷ 400 . About 10. In fact, 10.70603675...

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Estimate the quotient: 609,000 ÷ 16,000 size 12{"609,000 " div " 16,000"} {} .

609,000 ÷ 16,000 : 600,000 ÷ 15,000 . About 40. In fact, 38.0625.

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Sample set e

Estimate the sum: 53 . 82 + 41 . 6 size 12{"53" "." "82 "+" 41" "." 6} {} .

Notice that 53.82 is close to 54, two nonzero digits and that 41.6 is close to 42. two nonzero digits

The sum can be estimated by 54 + 42 = 96 size 12{"54 "+" 42 "=" 96"} {} .

Thus, 53 . 82 + 41 . 6 size 12{"53" "." "82 "+" 41" "." 6} {} is about 96. In fact, 53 . 82 + 41 . 6 = 95 . 42 size 12{"53" "." "82 "+" 41" "." "6 "=" 95" "." "42"} {} .

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Practice set e

Estimate the sum: 61 . 02 + 26 . 8 size 12{"61" "." "02 "+" 26" "." 8} {} .

61.02 + 26.8 : 61 + 27 . About 88. In fact, 87.82.

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Estimate the sum: 109 . 12 + 137 . 88 size 12{"109" "." "12 "+" 137" "." "88"} {} .

109.12 + 137.88 : 110 + 138 . About 248. In fact, 247. We could have estimated 137.88 with 140. Then 110 + 140 is an easy mental addition. We would conclude then that 109.12 + 137.88 is about 250.

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Sample set f

Estimate the product: ( 31 . 28 ) ( 14 . 2 ) size 12{ \( "31" "." "28" \) \( "14" "." 2 \) } {} .

Notice that 31.28 is close to 30, one nonzero digit and that 14.2 is close to 15. two nonzero digits

The product can be estimated by 30 15 = 450 size 12{"30 " cdot " 15 "=" 450"} {} . ( 3 15 = 45 size 12{"3 " cdot " 15 "=" 45"} {} , then affix one zero.)

Thus, ( 31 . 28 ) ( 14 . 2 ) size 12{ \( "31" "." "28" \) \( "14" "." 2 \) } {} is about 450. In fact, ( 31 . 28 ) ( 14 . 2 ) = 444 . 176 size 12{ \( "31" "." "28" \) \( "14" "." 2 \) =" 444" "." "176"} {} .

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Estimate 21% of 5.42.

Notice that 21% = . 21 size 12{"21% "= "." "21"} {} as a decimal, and that .21 is close to .2. one nonzero digit

Notice also that 5.42 is close to 5. one nonzero digit

Then, 21% of 5.42 can be estimated by ( . 2 ) ( 5 ) = 1 size 12{ \( "." 2 \) \( 5 \) =" 1"} {} .

Thus, 21% of 5.42 is about 1. In fact, 21% of 5.42 is 1.1382.

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Practice set f

Estimate the product: ( 47 . 8 ) ( 21 . 1 ) size 12{ \( "47" "." 8 \) \( "21" "." 1 \) } {} .

( 47.8 ) ( 21.1 ) : ( 50 ) ( 20 ) . About 1,000. In fact, 1,008.58.

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Estimate 32% of 14.88.

32% of 14.88 : ( .3 ) ( 15 ) . About 4.5. In fact, 4.7616.

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Exercises

Estimate each calculation using the method of rounding. After you have made an estimate, find the exact value and compare this to the estimated result to see if your estimated value is reasonable. Results may vary.

1, 402 + 2, 198 size 12{1,"402"+2,"198"} {}

about 3,600; in fact 3,600

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3,481 + 4,216 size 12{"3,481"+"4,216"} {}

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921 + 796 size 12{"921"+"796"} {}

about 1,700; in fact 1,717

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611 + 806 size 12{"611"+"806"} {}

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4, 681 + 9, 325 size 12{4,"681"+9,"325"} {}

about 14,000; in fact 14,006

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6, 476 + 7, 814 size 12{6,"476"+7,"814"} {}

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7, 805 4, 266 size 12{7,"805"-4,"266"} {}

about 3,500; in fact 3,539

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8, 427 5, 342 size 12{8,"427"-5,"342"} {}

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14 , 106 8, 412 size 12{"14","106"-8,"412"} {}

about 5,700; in fact 5,694

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26 , 486 18 , 931 size 12{"26","486"-"18","931"} {}

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32 53 size 12{"32" cdot "53"} {}

about 1,500; in fact 1,696

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67 42 size 12{"67" cdot "42"} {}

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628 891 size 12{"628" cdot "891"} {}

about 540,000; in fact 559,548

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426 741 size 12{"426" cdot "741"} {}

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18 , 012 32 , 416 size 12{"18","012" cdot "32","416"} {}

about 583,200,000; in fact 583,876,992

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22 , 481 51 , 076 size 12{"22","481" cdot "51","076"} {}

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287 ÷ 19 size 12{"287"÷"19"} {}

about 15; in fact 15.11

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884 ÷ 33 size 12{"884"÷"33"} {}

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1, 254 ÷ 57 size 12{1,"254"÷"57"} {}

about 20; in fact 22

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2, 189 ÷ 42 size 12{2,"189"÷"42"} {}

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8, 092 ÷ 239 size 12{8,"092"÷"239"} {}

about 33; in fact 33.86

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2, 688 ÷ 48 size 12{2,"688"÷"48"} {}

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72 . 14 + 21 . 08 size 12{"72" "." "14"+"21" "." "08"} {}

about 93.2; in fact 93.22

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43 . 016 + 47 . 58 size 12{"43" "." "016"+"47" "." "58"} {}

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96 . 53 26 . 91 size 12{"96" "." "53"-"26" "." "91"} {}

about 70; in fact 69.62

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115 . 0012 25 . 018 size 12{"115" "." "0012"-"25" "." "018"} {}

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206 . 19 + 142 . 38 size 12{"206" "." "19"+"142" "." "38"} {}

about 348.6; in fact 348.57

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592 . 131 + 211 . 6 size 12{"592" "." "131"+"211" "." 6} {}

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32 . 12 48 . 7 size 12{ left ("32" "." "12" right ) left ("48" "." 7 right )} {}

about 1,568.0; in fact 1,564.244

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87 . 013 21 . 07 size 12{ left ("87" "." "013" right ) left ("21" "." "07" right )} {}

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3 . 003 16 . 52 size 12{ left (3 "." "003" right ) left ("16" "." "52" right )} {}

about 49.5; in fact 49.60956

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6 . 032 14 . 091 size 12{ left (6 "." "032" right ) left ("14" "." "091" right )} {}

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114 . 06 384 . 3 size 12{ left ("114" "." "06" right ) left ("384" "." 3 right )} {}

about 43,776; in fact 43,833.258

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5, 137 . 118 263 . 56 size 12{ left (5,"137" "." "118" right ) left ("263" "." "56" right )} {}

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6 . 92 0 . 88 size 12{ left (6 "." "92" right ) left (0 "." "88" right )} {}

about 6.21; in fact 6.0896

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83 . 04 1 . 03 size 12{ left ("83" "." "04" right ) left (1 "." "03" right )} {}

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17 . 31 . 003 size 12{ left ("17" "." "31" right ) left ( "." "003" right )} {}

about 0.0519; in fact 0.05193

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14 . 016 . 016 size 12{ left ("14" "." "016" right ) left ( "." "016" right )} {}

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93 % of   7 . 01 size 12{"93""% of "7 "." "01"} {}

about 6.3; in fact 6.5193

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32% of 15.3

about 4.5; in fact 4.896

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18% of 4.118

about 0.8; in fact 0.74124

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2% of .0039

about 0.00008; in fact 0.000078

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Exercises for review

( [link] ) Find the difference: 7 10 5 16 . size 12{ { {7} over {"10"} } - { {5} over {"16"} } "." } {}

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( [link] ) Find the value 6 1 4 6 + 1 4 . size 12{ { {6- { {1} over {4} } } over {6+ { {1} over {4} } } } "." } {}

23 25 size 12{ { {"23"} over {"25"} } } {}

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( [link] ) Convert the complex decimal 1 . 11 1 4 size 12{1 "." "11" { {1} over {4} } } {} to a decimal.

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( [link] ) A woman 5 foot tall casts an 8-foot shadow at a particular time of the day. How tall is a tree that casts a 96-foot shadow at the same time of the day?

60 feet tall

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( [link] ) 11.62 is 83% of what number?

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Questions & Answers

What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
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
Do you know which machine is used to that process?
s.
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
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
Privacy Information Security Software Version 1.1a
Good
7hours 36 min - 4hours 50 min
Tanis 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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