<< Chapter < Page Chapter >> Page >
0.31 0.308
Convert to fractions. 31 100 308 1000
We need a common denominator to compare them. . .
310 1000 308 1000

Because 310>308, we know that 310 1000 > 308 1000 . Therefore, 0.31>0.308.

Notice what we did in converting 0.31 to a fraction—we started with the fraction 31 100 and ended with the equivalent fraction 310 1000 . Converting 310 1000 back to a decimal gives 0.310. So 0.31 is equivalent to 0.310. Writing zeros at the end of a decimal does not change its value!

31 100 = 310 1000 and 0.31 = 0.310

We say 0.31 and 0.310 are equivalent decimals    .

Equivalent decimals

Two decimals are equivalent if they convert to equivalent fractions.

We use equivalent decimals when we order decimals.

The steps we take to order decimals are summarized here.

Order decimals.

  1. Write the numbers one under the other, lining up the decimal points.
  2. Check to see if both numbers have the same number of digits. If not, write zeros at the end of the one with fewer digits to make them match.
  3. Compare the numbers as if they were whole numbers.
  4. Order the numbers using the appropriate inequality sign.

Order 0.64 ___ 0.6 using < or > .

Solution

Write the numbers one under the other, lining up the decimal points . 0.64 0.6 Add a zero to 0.6 to make it a decimal with 2 decimal places. 0.64 0.60 Now they are both hundredths. 64 is greater than 60. 64 > 60 64 hundredths is greater than 60 hundredths. 0.64 > 0.60 0.64 > 0.6

Got questions? Get instant answers now!
Got questions? Get instant answers now!

Order each of the following pairs of numbers, using < or > : 0.42 ___ 0.4 .

>

Got questions? Get instant answers now!

Order each of the following pairs of numbers, using < or > : 0.18 ___ 0.1 .

>

Got questions? Get instant answers now!

Order 0.83 ___ 0.803 using < or > .

Solution

0.83 ___ 0.803 Write the numbers one under the other, lining up the decimals. 0.83 0.803 They do not have the same number of digits. 0.830 0.803 Write one zero at the end of 0.83 . Since 830 > 803 , 830 thousandths is greater than 803 thousandths. 0.830 > 0.803 0.83 > 0.803

Got questions? Get instant answers now!
Got questions? Get instant answers now!

Order the following pair of numbers, using < or > : 0.76 ___ 0.706 .

>

Got questions? Get instant answers now!

Order the following pair of numbers, using < or > : 0.305 ___ 0.35 .

<

Got questions? Get instant answers now!

When we order negative decimals, it is important to remember how to order negative integers. Recall that larger numbers are to the right on the number line. For example, because −2 lies to the right of −3 on the number line, we know that −2 > −3 . Similarly, smaller numbers lie to the left on the number line. For example, because −9 lies to the left of −6 on the number line, we know that −9 < −6 . See [link] .

There is a number line shown that runs from negative 10 to 0. There are not points given and the hashmarks exist at every integer between negative 10 and 0.

If we zoomed in on the interval between 0 and −1 , as shown in [link] , we would see in the same way that −0.2 > −0.3 and 0.9 < −0.6 .

Use < or > to order −0.1 ___ −0.8 .

Solution

−0.1 ___ −0.8 Write the numbers one under the other, lining up the decimal points. 0.1 0.8 They have the same number of digits. Since −1 > −8 , −1 tenth is greater than −8 tenths. −0.1 > −0.8

Got questions? Get instant answers now!
Got questions? Get instant answers now!

Order the following pair of numbers, using<or>: −0.3 ___ −0.5 .

>

Got questions? Get instant answers now!

Order the following pair of numbers, using<or>: −0.6 ___ −0.7 .

>

Got questions? Get instant answers now!

Key concepts

  • Square Root Notation
    m is read ‘the square root of m .’ If m = n 2 , then m = n , for n 0 .
  • Order Decimals
    1. Write the numbers one under the other, lining up the decimal points.
    2. Check to see if both numbers have the same number of digits. If not, write zeros at the end of the one with fewer digits to make them match.
    3. Compare the numbers as if they were whole numbers.
    4. Order the numbers using the appropriate inequality sign.

Questions & Answers

a trader gains 20 rupees loses 42 rupees and then gains ten rupees Express algebraically the result of his transactions
vinaya Reply
a trader gains 20 rupees loses 42 rupees and then gains 10 rupees Express algebraically the result of his three transactions
vinaya
a trader gains 20 rupees loses 42 rupees and then gains 10 rupees Express algebraically the result of his three transactions
vinaya
a trader gains 20 rupees loses 42 rupees and then gains 10 rupees Express algebraically the result of his three transactions
vinaya
Kim is making eight gallons of punch from fruit juice and soda. The fruit juice costs $6.04 per gallon and the soda costs $4.28 per gallon. How much fruit juice and how much soda should she use so that the punch costs $5.71 per gallon?
Mohamed Reply
(a+b)(p+q+r)(b+c)(p+q+r)(c+a) (p+q+r)
muhammad Reply
4x-7y=8 2x-7y=1 what is the answer?
Ramil Reply
x=7/2 & y=6/7
Pbp
x=7/2 & y=6/7 use Elimination
Debra
true
bismark
factoriz e
usman
4x-7y=8 X=7/4y+2 and 2x-7y=1 x=7/2y+1/2
Peggie
Ok cool answer peggie
Frank
thanks
Ramil
copy and complete the table. x. 5. 8. 12. then 9x-5. to the 2nd power+4. then 2xto the second power +3x
Sandra Reply
What is c+4=8
Penny Reply
2
Letha
4
Lolita
4
Rich
4
thinking
C+4=8 -4 -4 C =4
thinking
I need to study
Letha
4+4=8
William
During two years in college, a student earned $9,500. The second year, she earned $500 more than twice the amount she earned the first year.
Nicole Reply
9500=500+2x
Debra
9500-500=9000 9000÷2×=4500 X=4500
Debra
X + Y = 9500....... & Y = 500 + 2X so.... X + 500 + 2X = 9500, them X = 3000 & Y = 6500
Pbp
Bruce drives his car for his job. The equation R=0.575m+42 models the relation between the amount in dollars, R, that he is reimbursed and the number of miles, m, he drives in one day. Find the amount Bruce is reimbursed on a day when he drives 220 miles.
Josh Reply
Reiko needs to mail her Christmas cards and packages and wants to keep her mailing costs to no more than $500. The number of cards is at least 4 more than twice the number of packages. The cost of mailing a card (with pictures enclosed) is $3 and for a package the cost is $7.
Ida Reply
hey
Juan
Sup
patrick
The sum of two numbers is 155. The difference is 23. Find the numbers
Michelle Reply
The sum of two numbers is 155. Their difference is 23. Find the numbers
Michelle
The difference between 89 and 66 is 23
Ciid
Joy is preparing 20 liters of a 25% saline solution. She only has 40% and 10% solution in her lab. How many liters of the 40% and how many liters of the 10% should she mix to make the 25% solution?
Amber Reply
hello
bismark
I need a math tutor BAD
Stacie
Me too
Letha
me too
Xavier
ok
Bishal
teet
Bishal
Sue and Deb work together writing a book that takes them 90 days. If Sue worked alone, it would take her 120 days. How long would it take Deb to write the book alone?
Hailey Reply
Tell Deb to write the book alone and report back on how long it took her. Deb could get bored and stop, she could get sick next week and prolong the time, she could die next month. This question is impossible to answer.
vV
right*
tyler
is there a thumbs up mathematical symbol in algebra? 👍²= vV 90days x 120days =10800 120days - 90days = 30 10800days/30days= 360days? (ad) derall=1440 mins (90x ad )+(120 x ad )/(120 x ad ))-((90d x ad)= you go glen coco! I'll see my self out
Nick
Larry and Tom were standing next to each other in the backyard when Tom challenged Larry to guess how tall he was. Larry knew his own height is 6.5 feet and when they measured their shadows, Larry’s shadow was 8 feet and Tom’s was 7.75 feet long. What is Tom’s height?
genevieve Reply
6.25
Ciid
6.25
Big
?
Twila
Wayne is hanging a string of lights 57 feet long around the three sides of his patio, which is adjacent to his house. the length of his patio, the side along the house, is 5 feet longer than twice it's width. Find the length and width of the patio.
Katherine Reply
complexed. could you please help me figure out?
Ciid
(sin=opp/adj) (tan= opp/adj) cos=hyp/adj
tyler
(sin=opp/adj) (tan= opp/adj) cos=hyp/adj dont quote me on it look it up
tyler
(sin=opp/adj) (tan= opp/adj) cos=hyp/adj dont quote me on it look it up
tyler
(sin=opp/adj) (tan= opp/adj) cos=hyp/adj dont quote me on it look it up
tyler
SOH = Sine is Opposite over Hypotenuse. CAH= Cosine is Adjacent over Hypotenuse. TOA = Tangent is Opposite over Adjacent.
tyler
H=57 and O=285 figure out what the adjacent?
tyler
help
Twila
draw a diagram first
John
Amara currently sells televisions for company A at a salary of $17,000 plus a $100 commission for each television she sells. Company B offers her a position with a salary of $29,000 plus a $20 commission for each television she sells. How many televisions would Amara need to sell for the options to be equal?
Marisol Reply
what is the quantity and price of the televisions for both options?
karl
Amara has to sell 120 televisions to make 29,000 of the salary of company B. 120 * TV 100= commission 12,000+ 17,000 = of company a salary 29,000 17000+
Ciid
Amara has to sell 120 televisions to make 29,000 of the salary of company B. 120 * TV 100= commission 12,000+ 17,000 = of company a salary 29,000
Ciid
Practice Key Terms 6

Get the best Elementary algebra course in your pocket!





Source:  OpenStax, Elementary algebra. OpenStax CNX. Jan 18, 2017 Download for free at http://cnx.org/content/col12116/1.2
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