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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

Discuss the differences between taste and flavor, including how other sensory inputs contribute to our  perception of flavor.
John Reply
taste refers to your understanding of the flavor . while flavor one The other hand is refers to sort of just a blend things.
Faith
While taste primarily relies on our taste buds, flavor involves a complex interplay between taste and aroma
Kamara
which drugs can we use for ulcers
Ummi Reply
omeprazole
Kamara
what
Renee
what is this
Renee
is a drug
Kamara
of anti-ulcer
Kamara
Omeprazole Cimetidine / Tagament For the complicated once ulcer - kit
Patrick
what is the function of lymphatic system
Nency Reply
Not really sure
Eli
to drain extracellular fluid all over the body.
asegid
The lymphatic system plays several crucial roles in the human body, functioning as a key component of the immune system and contributing to the maintenance of fluid balance. Its main functions include: 1. Immune Response: The lymphatic system produces and transports lymphocytes, which are a type of
asegid
to transport fluids fats proteins and lymphocytes to the blood stream as lymph
Adama
what is anatomy
Oyindarmola Reply
Anatomy is the identification and description of the structures of living things
Kamara
what's the difference between anatomy and physiology
Oyerinde Reply
Anatomy is the study of the structure of the body, while physiology is the study of the function of the body. Anatomy looks at the body's organs and systems, while physiology looks at how those organs and systems work together to keep the body functioning.
AI-Robot
what is enzymes all about?
Mohammed Reply
Enzymes are proteins that help speed up chemical reactions in our bodies. Enzymes are essential for digestion, liver function and much more. Too much or too little of a certain enzyme can cause health problems
Kamara
yes
Prince
how does the stomach protect itself from the damaging effects of HCl
Wulku Reply
little girl okay how does the stomach protect itself from the damaging effect of HCL
Wulku
it is because of the enzyme that the stomach produce that help the stomach from the damaging effect of HCL
Kamara
function of digestive system
Ali Reply
function of digestive
Ali
the diagram of the lungs
Adaeze Reply
what is the normal body temperature
Diya Reply
37 degrees selcius
Xolo
37°c
Stephanie
please why 37 degree selcius normal temperature
Mark
36.5
Simon
37°c
Iyogho
the normal temperature is 37°c or 98.6 °Fahrenheit is important for maintaining the homeostasis in the body the body regular this temperature through the process called thermoregulation which involves brain skin muscle and other organ working together to maintain stable internal temperature
Stephanie
37A c
Wulku
what is anaemia
Diya Reply
anaemia is the decrease in RBC count hemoglobin count and PVC count
Eniola
what is the pH of the vagina
Diya Reply
how does Lysin attack pathogens
Diya
acid
Mary
I information on anatomy position and digestive system and there enzyme
Elisha Reply
anatomy of the female external genitalia
Muhammad Reply
Organ Systems Of The Human Body (Continued) Organ Systems Of The Human Body (Continued)
Theophilus Reply
what's lochia albra
Kizito
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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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