<< Chapter < Page Chapter >> Page >

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"} {} .

Got questions? Get instant answers now!

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"} {} .

Got questions? Get instant answers now!

Practice set c

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

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

Got questions? Get instant answers now!

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

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

Got questions? Get instant answers now!

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

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

Got questions? Get instant answers now!

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"} {} .

Got questions? Get instant answers now!

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}} } {} .

Got questions? Get instant answers now!

Practice set d

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

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

Got questions? Get instant answers now!

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

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

Got questions? Get instant answers now!

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.

Got questions? Get instant answers now!

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"} {} .

Got questions? Get instant answers now!

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.

Got questions? Get instant answers now!

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.

Got questions? Get instant answers now!

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"} {} .

Got questions? Get instant answers now!

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.

Got questions? Get instant answers now!

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.

Got questions? Get instant answers now!

Estimate 32% of 14.88.

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

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

about 1,700; in fact 1,717

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

about 14,000; in fact 14,006

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

about 3,500; in fact 3,539

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

about 5,700; in fact 5,694

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

about 1,500; in fact 1,696

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

about 540,000; in fact 559,548

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

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

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

287 ÷ 19 size 12{"287"÷"19"} {}

about 15; in fact 15.11

Got questions? Get instant answers now!

884 ÷ 33 size 12{"884"÷"33"} {}

Got questions? Get instant answers now!

1, 254 ÷ 57 size 12{1,"254"÷"57"} {}

about 20; in fact 22

Got questions? Get instant answers now!

2, 189 ÷ 42 size 12{2,"189"÷"42"} {}

Got questions? Get instant answers now!

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

about 33; in fact 33.86

Got questions? Get instant answers now!

2, 688 ÷ 48 size 12{2,"688"÷"48"} {}

Got questions? Get instant answers now!

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

about 93.2; in fact 93.22

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

about 70; in fact 69.62

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

about 348.6; in fact 348.57

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

about 1,568.0; in fact 1,564.244

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

about 49.5; in fact 49.60956

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

about 43,776; in fact 43,833.258

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

about 6.21; in fact 6.0896

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

about 0.0519; in fact 0.05193

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

about 6.3; in fact 6.5193

Got questions? Get instant answers now!

32% of 15.3

about 4.5; in fact 4.896

Got questions? Get instant answers now!

18% of 4.118

about 0.8; in fact 0.74124

Got questions? Get instant answers now!

2% of .0039

about 0.00008; in fact 0.000078

Got questions? Get instant answers now!

Exercises for review

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

Got questions? Get instant answers now!

( [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"} } } {}

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

( [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

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

Questions & Answers

what is biology
Hajah Reply
the study of living organisms and their interactions with one another and their environments
AI-Robot
what is biology
Victoria Reply
HOW CAN MAN ORGAN FUNCTION
Alfred Reply
the diagram of the digestive system
Assiatu Reply
allimentary cannel
Ogenrwot
How does twins formed
William Reply
They formed in two ways first when one sperm and one egg are splited by mitosis or two sperm and two eggs join together
Oluwatobi
what is genetics
Josephine Reply
Genetics is the study of heredity
Misack
how does twins formed?
Misack
What is manual
Hassan Reply
discuss biological phenomenon and provide pieces of evidence to show that it was responsible for the formation of eukaryotic organelles
Joseph Reply
what is biology
Yousuf Reply
the study of living organisms and their interactions with one another and their environment.
Wine
discuss the biological phenomenon and provide pieces of evidence to show that it was responsible for the formation of eukaryotic organelles in an essay form
Joseph Reply
what is the blood cells
Shaker Reply
list any five characteristics of the blood cells
Shaker
lack electricity and its more savely than electronic microscope because its naturally by using of light
Abdullahi Reply
advantage of electronic microscope is easily and clearly while disadvantage is dangerous because its electronic. advantage of light microscope is savely and naturally by sun while disadvantage is not easily,means its not sharp and not clear
Abdullahi
cell theory state that every organisms composed of one or more cell,cell is the basic unit of life
Abdullahi
is like gone fail us
DENG
cells is the basic structure and functions of all living things
Ramadan
What is classification
ISCONT Reply
is organisms that are similar into groups called tara
Yamosa
in what situation (s) would be the use of a scanning electron microscope be ideal and why?
Kenna Reply
A scanning electron microscope (SEM) is ideal for situations requiring high-resolution imaging of surfaces. It is commonly used in materials science, biology, and geology to examine the topography and composition of samples at a nanoscale level. SEM is particularly useful for studying fine details,
Hilary
cell is the building block of life.
Condoleezza 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