<< Chapter < Page Chapter >> Page >
This module is from Elementary Algebra by Denny Burzynski and Wade Ellis, Jr. This chapter contains many examples of arithmetic techniques that are used directly or indirectly in algebra. Since the chapter is intended as a review, the problem-solving techniques are presented without being developed. Therefore, no work space is provided, nor does the chapter contain all of the pedagogical features of the text. As a review, this chapter can be assigned at the discretion of the instructor and can also be a valuable reference tool for the student.

Overview

  • Decimal Fractions
  • Adding and Subtracting Decimal Fractions
  • Multiplying Decimal Fractions
  • Dividing Decimal Fractions
  • Converting Decimal Fractions to Fractions
  • Converting Fractions to Decimal Fractions

Decimal fractions

Fractions are one way we can represent parts of whole numbers. Decimal fractions are another way of representing parts of whole numbers.

Decimal fractions

A decimal fraction is a fraction in which the denominator is a power of 10.

A decimal fraction uses a decimal point to separate whole parts and fractional parts. Whole parts are written to the left of the decimal point and fractional parts are written to the right of the decimal point. Just as each digit in a whole number has a particular value, so do the digits in decimal positions.

The positions of the digits lying to the left and to the right of the decimal point are labeled. Moving towards left from the decimal point, the positions are labeled: the first as 'ones', the second as 'Tens', the third as 'Hundreds', the fourth as 'Thousands', the fifth as 'Ten Thousands', the sixth as 'Hundred Thousands', and the seventh as 'Millions'. Moving towards right from the decimal point, the positions are labeled: the first position as 'Tenths', the second position as 'Hundredths', the third as 'Thousandths', the fourth as 'Ten Thousandths', the fifth as 'Hundred Thousandths', and the sixth position as 'Millionths'. There is a comment written below the decimal positons as

Sample set a

The following numbers are decimal fractions.

57.9 The 9 is in the t e n t h s position . 57.9 = 57 9 10 .

Got questions? Get instant answers now!

6.8014 The 8 is in the  t e n t h s  position .  The 0 is in the  h u n d r e d t h s  position .  The 1 is in the  t h o u s a n d t h s  position .  The 4 is in the ten  t h o u s a n d t h s  position .  6.8014 = 6 8014 10000 .

Got questions? Get instant answers now!

Adding and subtracting decimal fractions

Adding/subtracting decimal fractions

To add or subtract decimal fractions,
  1. Align the numbers vertically so that the decimal points line up under each other and corresponding decimal positions are in the same column. Add zeros if necessary.
  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 b

Find each sum or difference.

9.183 + 2.140 The decimal points are aligned in the same column .  9 .183 +  2 .140 ¯ 11 .323

Got questions? Get instant answers now!

841.0056 + 47.016 + 19.058 The decimal points are aligned in the same column .  841.0056 47.016 Place a 0 into the thousandths position . + 19.058 ¯ Place a 0 into the thousandths position .  The decimal points are aligned in the same column .  841.0056 47.0160 + 19.0580 ¯ 907.0796

Got questions? Get instant answers now!

16.01 7.053 The decimal points are aligned in the same column .  16.01 Place a 0 into the thousandths position .  7.053 ¯ The decimal points are aligned in the same column .  16.010 7.053 ¯ 8.957

Got questions? Get instant answers now!

Multiplying decimal fractions

Multiplying decimal fractions

To multiply decimals,
  1. Multiply tbe numbers as if they were whole numbers.
  2. Find the sum of the number of decimal places in the factors.
  3. The number of decimal places in the product is the sum found in step 2.

Sample set c

Find the following products.

6.5 × 4.3

The vertical multiplication of two decimals; six point five, and four point three. See the longdesc for a full description.

6.5 × 4.3 = 27.95

Got questions? Get instant answers now!

23.4 × 1.96

The vertical multiplication of two decimals; twenty-three point four, and one point nine six. See the longdesc for a full description.

23.4 × 1.96 = 45.864

Got questions? Get instant answers now!

Dividing decimal fractions

Dividing decimal fractions

To divide a decimal by a nonzero decimal,
  1. Convert the divisor to a whole number by moving the decimal point to the position immediately to the right of the divisor’s last digit.
  2. Move the decimal point of the dividend to the right the same number of digits it was moved in the divisor.
  3. Set the decimal point in the quotient by placing a decimal point directly above the decimal point in the dividend.
  4. Divide as usual.

Sample set d

Find the following quotients.

32.66 ÷ 7.1

A long division problem showing seven point one dividing thirty-two point six six. See the longdesc for a full description.

32.66 ÷ 7.1 = 4.6 C h e c k : 32.66 ÷ 7.1 = 4.6 if 4.6 × 7.1 = 32.66 4.6 7.1 ¯ 4.6 322 ¯ 32.66 True

Got questions? Get instant answers now!

A long division problem showing zero point five one three dividing one point zero seven seven three. See the longdesc for a full description.

Check by multiplying 2.1 and 0.513. This will show that we have obtained the correct result.

Got questions? Get instant answers now!

Converting decimal fractions to fractions

We can convert a decimal fraction to a fraction by reading it and then writing the phrase we have just read. As we read the decimal fraction, we note the place value farthest to the right. We may have to reduce the fraction.

Sample set e

Convert each decimal fraction to a fraction.

0.6 0. 6 ¯ tenths position Reading: six tenths 6 10 Reduce: 0.6 = 6 10 = 3 5

Got questions? Get instant answers now!

21.903 21.90 3 ¯ thousandths position Reading: twenty-one and nine hundred three thousandths 21 903 1000

Got questions? Get instant answers now!

Converting fractions to decimal fractions

Sample set f

Convert the following fractions to decimals. If the division is nonterminating, round to 2 decimal places.

5 6

A long division problem showing six dividing five point zero zero zero. See the longdesc for a full description.

5 6 = 0.833... We are to round to 2 decimal places . 5 6 = 0.83  to 2 decimal places .

Got questions? Get instant answers now!

5 1 8 Note that  5 1 8 = 5 + 1 8 .

One point zero zero zero is being divided by eight, using long division method. See the longdesc for a full description.

1 8 = .125 Thus,  5 1 8 = 5 + 1 8 = 5 + .125 = 5.125.

Got questions? Get instant answers now!

0.16 1 4

This is a complex decimal. The “6” is in the hundredths position. The number 0.16 1 4 is read as “sixteen and one-fourth hundredths.”

0.16 1 4 = 16 1 4 100 = 16 · 4 + 1 4 100 = 65 4 100 1 = 65 13 4 · 1 100 20 = 13 × 1 4 × 20 = 13 80

Now, convert 13 80 to a decimal.

Thirteen point zero zero zero zero is being divided by eighty, using long division method. See the longdesc for a full description.

0.16 1 4 = 0.1625.

Got questions? Get instant answers now!

Exercises

For the following problems, perform each indicated operation.

.0012 + 1.53 + 5.1

6.6312

Got questions? Get instant answers now!

5.0004 3.00004 + 1.6837

3.68406

Got questions? Get instant answers now!

1.11 + 12.1212 13.131313

Got questions? Get instant answers now!

4.26 · 3.2

13.632

Got questions? Get instant answers now!

23.05 · 1.1

25.355

Got questions? Get instant answers now!

0.1 · 3.24

0.324

Got questions? Get instant answers now!

1000 · 12.008

12 , 008

Got questions? Get instant answers now!

10 , 000 · 12.008

Got questions? Get instant answers now!

75.642 ÷ 18.01

4.2

Got questions? Get instant answers now!

0.0000448 ÷ 0.014

0.0032

Got questions? Get instant answers now!

0.129516 ÷ 1004

Got questions? Get instant answers now!

For the following problems, convert each decimal fraction to a fraction.

For the following problems, convert each fraction to a decimal fraction. If the decimal form is nonterminating,round to 3 decimal places.

Questions & Answers

what is math number
Tric Reply
x-2y+3z=-3 2x-y+z=7 -x+3y-z=6
Sidiki Reply
Need help solving this problem (2/7)^-2
Simone Reply
x+2y-z=7
Sidiki
what is the coefficient of -4×
Mehri Reply
-1
Shedrak
the operation * is x * y =x + y/ 1+(x × y) show if the operation is commutative if x × y is not equal to -1
Alfred Reply
An investment account was opened with an initial deposit of $9,600 and earns 7.4% interest, compounded continuously. How much will the account be worth after 15 years?
Kala Reply
lim x to infinity e^1-e^-1/log(1+x)
given eccentricity and a point find the equiation
Moses Reply
12, 17, 22.... 25th term
Alexandra Reply
12, 17, 22.... 25th term
Akash
College algebra is really hard?
Shirleen Reply
Absolutely, for me. My problems with math started in First grade...involving a nun Sister Anastasia, bad vision, talking & getting expelled from Catholic school. When it comes to math I just can't focus and all I can hear is our family silverware banging and clanging on the pink Formica table.
Carole
I'm 13 and I understand it great
AJ
I am 1 year old but I can do it! 1+1=2 proof very hard for me though.
Atone
hi
Adu
Not really they are just easy concepts which can be understood if you have great basics. I am 14 I understood them easily.
Vedant
find the 15th term of the geometric sequince whose first is 18 and last term of 387
Jerwin Reply
I know this work
salma
The given of f(x=x-2. then what is the value of this f(3) 5f(x+1)
virgelyn Reply
hmm well what is the answer
Abhi
If f(x) = x-2 then, f(3) when 5f(x+1) 5((3-2)+1) 5(1+1) 5(2) 10
Augustine
how do they get the third part x = (32)5/4
kinnecy Reply
make 5/4 into a mixed number, make that a decimal, and then multiply 32 by the decimal 5/4 turns out to be
AJ
how
Sheref
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
hmm
Abhi
is it a question of log
Abhi
🤔.
Abhi
I rally confuse this number And equations too I need exactly help
salma
But this is not salma it's Faiza live in lousvile Ky I garbage this so I am going collage with JCTC that the of the collage thank you my friends
salma
Commplementary angles
Idrissa Reply
hello
Sherica
im all ears I need to learn
Sherica
right! what he said ⤴⤴⤴
Tamia
hii
Uday
hi
salma
hi
Ayuba
Hello
opoku
hi
Ali
greetings from Iran
Ali
salut. from Algeria
Bach
hi
Nharnhar
A soccer field is a rectangle 130 meters wide and 110 meters long. The coach asks players to run from one corner to the other corner diagonally across. What is that distance, to the nearest tenths place.
Kimberly Reply
Jeannette has $5 and $10 bills in her wallet. The number of fives is three more than six times the number of tens. Let t represent the number of tens. Write an expression for the number of fives.
August Reply
What is the expressiin for seven less than four times the number of nickels
Leonardo Reply
How do i figure this problem out.
how do you translate this in Algebraic Expressions
linda Reply
why surface tension is zero at critical temperature
Shanjida
I think if critical temperature denote high temperature then a liquid stats boils that time the water stats to evaporate so some moles of h2o to up and due to high temp the bonding break they have low density so it can be a reason
s.
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
Please keep in mind that it's not allowed to promote any social groups (whatsapp, facebook, etc...), exchange phone numbers, email addresses or ask for personal information on QuizOver's platform.
QuizOver Reply

Get the best Algebra and trigonometry course in your pocket!





Source:  OpenStax, Elementary algebra. OpenStax CNX. May 08, 2009 Download for free at http://cnx.org/content/col10614/1.3
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Elementary algebra' conversation and receive update notifications?

Ask