<< Chapter < Page Chapter >> Page >
This module is from Fundamentals of Mathematics by Denny Burzynski and Wade Ellis, Jr. This module discusses how to add and subtract decimals. By the end of the module students should understand the method used for adding and subtracting decimals, be able to add and subtract decimals and be able to use the calculator to add and subtract decimals.

Section overview

  • The Logic Behind the Method
  • The Method of Adding and Subtracting Decimals
  • Calculators

The logic behind the method

Consider the sum of 4.37 and 3.22. Changing each decimal to a fraction, we have

4 37 100 + 3 22 100 size 12{4 { {"37"} over {"100"} } +3 { {"22"} over {"100"} } " Performing the addition, we get"} {} Performing the addition, we get

4 . 37 + 3 . 22 = 4 37 100 + 3 22 100 = 4 100 + 37 100 + 3 100 + 22 100 = 437 100 + 322 100 = 437 + 322 100 = 759 100 = 7 59 100 = seven and fifty-nine hundredths = 7.59

Thus, 4 . 37 + 3 . 22 = 7 . 59 size 12{4 "." "37 "+" 3" "." "22 "=" 7" "." "59"} {} .

The method of adding and subtracting decimals

When writing the previous addition, we could have written the numbers in col­umns.

4.37 + 3.22 ̲ 7.59

This agrees with our previous result. From this observation, we can suggest a method for adding and subtracting decimal numbers.

Method of adding and subtracting decimals

To add or subtract decimals:
  1. Align the numbers vertically so that the decimal points line up under each other and the corresponding decimal positions are in the same column.
  2. Add or subtract the numbers as if they were whole numbers.
  3. Place a decimal point in the resulting sum or difference directly under the other decimal points.

Sample set a

Find the following sums and differences.

9 . 813 + 2 . 140 size 12{9 "." "813"+2 "." "140"} {}

9.813 The decimal points are aligned in the same column. + 2.140 ̲ 11.953

841 . 0056 + 47 . 016 + 19 . 058 size 12{"841" "." "0056"+"47" "." "016"+"19" "." "058"} {}

841.0056 47.016   + 19.058   ̲

To insure that the columns align properly, we can write a 0 in the position at the end of the numbers 47.016 and 19.058 without changing their values.

Vertical addition. 841.0056 plus 47.0160 plus 19.0580 equals 907.0796. A 1 needed to be carried in the hundredths, the tens, and the hundreds columns.

1.314 - 0.58

1.314 - 0.58   ̲ Write a 0 in the thousandths position.

Vertical subtraction. 1.314 minus 0.580 equals 0.734. The ones, and hundredths digits need to be borrowed from once, and the tenths needs to be borrowed from twice to perform the subtraction.

16.01 - 7.053

16.01   - 7.053 ̲ Write a 0 in the thousandths position.

Vertical subtraction. 16.101 minus 7.053 equals 8.957. The ones, tenths, hundredths, and thousandths digits need to be borrowed from once to perform the subtraction.

Find the sum of 6.88106 and 3.5219 and round it to three decimal places.

6.88106 + 3.5219   ̲ Write a 0 in the ten thousandths position.

Vertical addition. 6.88106 plus 3.52190 equals 10.40296. A 1 needs to be carried over the tenths and ones digits to perform the addition.

We need to round the sum to the thousandths position. Since the digit in the position immediately to the right is 9, and 9>5, we get

10.403

Wendy has $643.12 in her checking account. She writes a check for $16.92. How much is her new account balance?

To find the new account balance, we need to find the difference between 643.12 and 16.92. We will subtract 16.92 from 643.12.

Vertical subtraction. 643.12 minus 16.92 equals 626.20.

After writing a check for $16.92, Wendy now has a balance of $626.20 in her checking account.

Practice set a

Find the following sums and differences.

3 . 187 + 2 . 992 size 12{3 "." "187 "+" 2" "." "992"} {}

6.179

14 . 987 - 5 . 341 size 12{"14" "." "987 - 5" "." "341"} {}

9.646

0 . 5261 + 1 . 0783 size 12{0 "." "5261 "+" 1" "." "0783"} {}

1.6044

1.06 - 1.0535 size 12{1 "." "06 - 1" "." "0535"} {}

0.0065

16,521 . 07 + 9,256 . 15 size 12{"16,521" "." "07 "+" 9,256" "." "15"} {}

25,777.22

Find the sum of 11.6128 and 14.07353, and round it to two decimal places.

25.69

Calculators

The calculator can be useful for finding sums and differences of decimal numbers. However, calculators with an eight-digit display cannot be used when working with decimal numbers that contain more than eight digits, or when the sum results in more than eight digits. In practice, an eight-place decimal will seldom be encoun­tered. There are some inexpensive calculators that can handle 13 decimal places.

Sample set b

Use a calculator to find each sum or difference.

42.0638 + 126.551

Display Reads
Type 42.0638 42.0638
Press + 42.0638
Type 126.551 126.551
Press = 168.6148

The sum is 168.6148.

Find the difference between 305.0627 and 14.29667.

Display Reads
Type 305.0627 305.0627
Press 305.0627
Type 14.29667 14.29667
Press = 290.76603

The difference is 290.76603

51.07 + 3,891.001786

Since 3,891.001786 contains more than eight digits, we will be unable to use an eight-digit display calculator to perform this addition. We can, however, find the sum by hand.

51.070000 3891.001786 ̲ 3942.071786

The sum is 3,942.071786.

Practice set b

Use a calculator to perform each operation.

4 . 286 + 8 . 97 size 12{4 "." "286 "+" 8" "." "97"} {}

13.256

452.0092 - 392.558 size 12{"452" "." "0092 - 392" "." "558"} {}

59.4512

Find the sum of 0.095 and 0.001862

0.096862

Find the difference between 0.5 and 0.025

0.475

Find the sum of 2,776.00019 and 2,009.00012.

Since each number contains more than eight digits, using some calculators may not be helpful. Adding these by “hand technology,” we get 4,785.00031

Exercises

For the following 15 problems, perform each addition or subtraction. Use a calculator to check each result.

1 . 84 + 7 . 11 size 12{1 "." "84"+7 "." "11"} {}

8.95

15 . 015 6 . 527 size 12{"15" "." "015"-6 "." "527"} {}

11 . 842 + 28 . 004 size 12{"11" "." "842"+"28" "." "004"} {}

39.846

3 . 16 2 . 52 size 12{3 "." "16"-2 "." "52"} {}

3 . 55267 + 8 . 19664 size 12{3 "." "55267"+8 "." "19664"} {}

11.74931

0 . 9162 0 . 0872 size 12{0 "." "9162"-0 "." "0872"} {}

65 . 512 8 . 3005 size 12{"65" "." "512"-8 "." "3005"} {}

57.2115

761 . 0808 53 . 198 size 12{"761" "." "0808"-"53" "." "198"} {}

4 . 305 + 2 . 119 3 . 817 size 12{4 "." "305"+2 "." "119"-3 "." "817"} {}

2.607

19 . 1161 + 27 . 8014 + 39 . 3161 size 12{"19" "." "1161"+"27" "." "8014"+"39" "." "3161"} {}

0 . 41276 0 . 0018 0 . 00011 size 12{0 "." "41276"-0 "." "0018"-0 "." "00011"} {}

0.41085

2 . 181 + 6 . 05 + 1 . 167 + 8 . 101 size 12{2 "." "181"+6 "." "05"+1 "." "167"+8 "." "101"} {}

1.0031+6.013106+0.00018+0.0092+2.11

9.135586

27 + 42 + 9 . 16 0 . 1761 + 81 . 6 size 12{"27"+"42"+9 "." "16"-0 "." "1761"+"81" "." 6} {}

10 . 28 + 11 . 111 + 0 . 86 + 5 . 1 size 12{"10" "." "28"+"11" "." "111"+0 "." "86"+5 "." 1} {}

27.351

For the following 10 problems, solve as directed. A calculator may be useful.

Add 6.1121 and 4.916 and round to 2 decimal places.

Add 21.66418 and 18.00184 and round to 4 decimal places.

39.6660

Subtract 5.2121 from 9.6341 and round to 1 decimal place.

Subtract 0.918 from 12.006 and round to 2 decimal places.

11.09

Subtract 7.01884 from the sum of 13.11848 and 2.108 and round to 4 decimal places.

A checking account has a balance of $42.51. A check is written for $19.28. What is the new balance?

$23.23

A checking account has a balance of $82.97. One check is written for $6.49 and another for $39.95. What is the new balance?

A person buys $4.29 worth of hamburger and pays for it with a $10 bill. How much change does this person get?

$5.71

A man buys $6.43 worth of stationary and pays for it with a $20 bill. After receiving his change, he realizes he forgot to buy a pen. If the total price of the pen is $2.12, and he buys it, how much of the $20 bill is left?

A woman starts recording a movie on her video cassette recorder with the tape counter set at 21.93. The movie runs 847.44 tape counter units. What is the final tape counter reading?

869.37

Exercises for review

( [link] ) Find the difference between 11,206 and 10,884.

( [link] ) Find the product, 820 10,000 size 12{"820 " cdot " 10,000"} {} .

8,200,000

( [link] ) Find the value of 121 25 + 8 2 + 16 ÷ 2 2 size 12{ sqrt {"121"} - sqrt {"25"} +8 rSup { size 8{2} } +"16" div 2 rSup { size 8{2} } } {} .

( [link] ) Find the value of 8 1 3 36 75 ÷ 2 2 5 size 12{8 { {1} over {3} } cdot { {"36"} over {"75"} } div 2 { {2} over {5} } } {} .

20 9 = 5 3  or  2 2 9 size 12{ { {"20"} over {9} } = { {5} over {3} } " or " { {2} over {9} } } {}

( [link] ) Round 1.08196 to the nearest hundredth.

Questions & Answers

can someone help me with some logarithmic and exponential equations.
Jeffrey Reply
sure. what is your question?
ninjadapaul
20/(×-6^2)
Salomon
okay, so you have 6 raised to the power of 2. what is that part of your answer
ninjadapaul
I don't understand what the A with approx sign and the boxed x mean
ninjadapaul
it think it's written 20/(X-6)^2 so it's 20 divided by X-6 squared
Salomon
I'm not sure why it wrote it the other way
Salomon
I got X =-6
Salomon
ok. so take the square root of both sides, now you have plus or minus the square root of 20= x-6
ninjadapaul
oops. ignore that.
ninjadapaul
so you not have an equal sign anywhere in the original equation?
ninjadapaul
Commplementary angles
Idrissa Reply
hello
Sherica
im all ears I need to learn
Sherica
right! what he said ⤴⤴⤴
Tamia
what is a good calculator for all algebra; would a Casio fx 260 work with all algebra equations? please name the cheapest, thanks.
Kevin Reply
a perfect square v²+2v+_
Dearan Reply
kkk nice
Abdirahman Reply
algebra 2 Inequalities:If equation 2 = 0 it is an open set?
Kim Reply
or infinite solutions?
Kim
The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
Al
y=10×
Embra Reply
if |A| not equal to 0 and order of A is n prove that adj (adj A = |A|
Nancy Reply
rolling four fair dice and getting an even number an all four dice
ramon Reply
Kristine 2*2*2=8
Bridget Reply
Differences Between Laspeyres and Paasche Indices
Emedobi Reply
No. 7x -4y is simplified from 4x + (3y + 3x) -7y
Mary Reply
is it 3×y ?
Joan Reply
J, combine like terms 7x-4y
Bridget Reply
im not good at math so would this help me
Rachael Reply
yes
Asali
I'm not good at math so would you help me
Samantha
what is the problem that i will help you to self with?
Asali
how do you translate this in Algebraic Expressions
linda Reply
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
Crystal Reply
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
Chris 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
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
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
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
bamidele Reply
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
Got questions? Join the online conversation and get instant answers!
QuizOver.com Reply

Get the best Algebra and trigonometry course in your pocket!





Source:  OpenStax, Contemporary math applications. OpenStax CNX. Dec 15, 2014 Download for free at http://legacy.cnx.org/content/col11559/1.6
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Contemporary math applications' conversation and receive update notifications?

Ask