<< 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

Got questions? Get instant answers now!

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.

Got questions? Get instant answers now!

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.

Got questions? Get instant answers now!

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.

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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.

Got questions? Get instant answers now!

Practice set a

Find the following sums and differences.

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

6.179

Got questions? Get instant answers now!

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

9.646

Got questions? Get instant answers now!

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

1.6044

Got questions? Get instant answers now!

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

0.0065

Got questions? Get instant answers now!

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

25,777.22

Got questions? Get instant answers now!

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

25.69

Got questions? Get instant answers now!

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.

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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.

Got questions? Get instant answers now!

Practice set b

Use a calculator to perform each operation.

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

13.256

Got questions? Get instant answers now!

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

59.4512

Got questions? Get instant answers now!

Find the sum of 0.095 and 0.001862

0.096862

Got questions? Get instant answers now!

Find the difference between 0.5 and 0.025

0.475

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

39.846

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

11.74931

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

57.2115

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

2.607

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

0.41085

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

1.0031+6.013106+0.00018+0.0092+2.11

9.135586

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

27.351

Got questions? Get instant answers now!

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.

Got questions? Get instant answers now!

Add 21.66418 and 18.00184 and round to 4 decimal places.

39.6660

Got questions? Get instant answers now!

Subtract 5.2121 from 9.6341 and round to 1 decimal place.

Got questions? Get instant answers now!

Subtract 0.918 from 12.006 and round to 2 decimal places.

11.09

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

$23.23

Got questions? Get instant answers now!

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?

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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?

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

Exercises for review

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

Got questions? Get instant answers now!

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

8,200,000

Got questions? Get instant answers now!

( [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} } } {} .

Got questions? Get instant answers now!

( [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} } } {}

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

Questions & Answers

What is inflation
Bright Reply
a general and ongoing rise in the level of prices in an economy
AI-Robot
What are the factors that affect demand for a commodity
Florence Reply
differentiate between demand and supply giving examples
Lambiv Reply
differentiated between demand and supply using examples
Lambiv
what is labour ?
Lambiv
how will I do?
Venny Reply
how is the graph works?I don't fully understand
Rezat Reply
information
Eliyee
devaluation
Eliyee
t
WARKISA
hi guys good evening to all
Lambiv
multiple choice question
Aster Reply
appreciation
Eliyee
explain perfect market
Lindiwe Reply
In economics, a perfect market refers to a theoretical construct where all participants have perfect information, goods are homogenous, there are no barriers to entry or exit, and prices are determined solely by supply and demand. It's an idealized model used for analysis,
Ezea
What is ceteris paribus?
Shukri Reply
other things being equal
AI-Robot
When MP₁ becomes negative, TP start to decline. Extuples Suppose that the short-run production function of certain cut-flower firm is given by: Q=4KL-0.6K2 - 0.112 • Where is quantity of cut flower produced, I is labour input and K is fixed capital input (K-5). Determine the average product of lab
Kelo
Extuples Suppose that the short-run production function of certain cut-flower firm is given by: Q=4KL-0.6K2 - 0.112 • Where is quantity of cut flower produced, I is labour input and K is fixed capital input (K-5). Determine the average product of labour (APL) and marginal product of labour (MPL)
Kelo
yes,thank you
Shukri
Can I ask you other question?
Shukri
what is monopoly mean?
Habtamu Reply
What is different between quantity demand and demand?
Shukri Reply
Quantity demanded refers to the specific amount of a good or service that consumers are willing and able to purchase at a give price and within a specific time period. Demand, on the other hand, is a broader concept that encompasses the entire relationship between price and quantity demanded
Ezea
ok
Shukri
how do you save a country economic situation when it's falling apart
Lilia Reply
what is the difference between economic growth and development
Fiker Reply
Economic growth as an increase in the production and consumption of goods and services within an economy.but Economic development as a broader concept that encompasses not only economic growth but also social & human well being.
Shukri
production function means
Jabir
What do you think is more important to focus on when considering inequality ?
Abdisa Reply
any question about economics?
Awais Reply
sir...I just want to ask one question... Define the term contract curve? if you are free please help me to find this answer 🙏
Asui
it is a curve that we get after connecting the pareto optimal combinations of two consumers after their mutually beneficial trade offs
Awais
thank you so much 👍 sir
Asui
In economics, the contract curve refers to the set of points in an Edgeworth box diagram where both parties involved in a trade cannot be made better off without making one of them worse off. It represents the Pareto efficient allocations of goods between two individuals or entities, where neither p
Cornelius
In economics, the contract curve refers to the set of points in an Edgeworth box diagram where both parties involved in a trade cannot be made better off without making one of them worse off. It represents the Pareto efficient allocations of goods between two individuals or entities,
Cornelius
Suppose a consumer consuming two commodities X and Y has The following utility function u=X0.4 Y0.6. If the price of the X and Y are 2 and 3 respectively and income Constraint is birr 50. A,Calculate quantities of x and y which maximize utility. B,Calculate value of Lagrange multiplier. C,Calculate quantities of X and Y consumed with a given price. D,alculate optimum level of output .
Feyisa Reply
Answer
Feyisa
c
Jabir
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