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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

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

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

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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

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

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

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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

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

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

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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

how to square
Fiona Reply
easiest way to find the square root of a large number?
Jackie
the accompanying figure shows known flow rates of hydrocarbons into and out of a network of pipes at an oil refinery set up a linear system whose solution provides the unknown flow rates (b) solve the system for the unknown flow rates (c) find the flow rates and directions of flow if x4=50and x6=0
Sabee Reply
What is observation
adeyemi Reply
I'm confused by the question. Can you describe or explain the math question it pertains to?
Melissa
there is no math to it because all you use is your vision or gaze to the sorrounding areas
Cesarp
Teegan likes to play golf. He has budgeted $60 next month for the driving range. It costs him $10.55 for a bucket of balls each time he goes. What is the maximum number of times he can go to the driving range next month?
Sunnyshay Reply
5 times max
Anton
Felecia left her home to visit her daughter, driving 45mph. Her husband waited for the dog sitter to arrive and left home 20 minutes, or 1/3 hour later. He drove 55mph to catch up to Felecia. How long before he reaches her?
Sophia Reply
35 min
Debra
Carmen wants to tile the floor of his house. He will need 1,000 square feet of tile. He will do most of the floor with a tile that costs $1.50 per square foot, but also wants to use an accent tile that costs $9.00 per square foot. How many square feet of each tile should he plan to use if he wants the overall cost to be $3 per square foot?
Parker Reply
what you wanna get
Cesar
800 sq. ft @ $1.50 & 200 sq. ft @ $9.00
Marco
Geneva treated her parents to dinner at their favorite restaurant. The bill was $74.25. Geneva wants to leave 16 % of the total - bill as a tip. How much should the tip be?
74.25 × .16 then get the total and that will be your tip
David
$74.25 x 0.16 = $11.88 total bill: $74.25 + $11.88 = $86.13
ericka
yes and tip 16% will be $11.88
David
what is the shorter way to do it
Cesar Reply
Priam has dimes and pennies in a cup holder in his car. The total value of the coins is $4.21. The number of dimes is three less than four times the number of pennies. How many dimes and how many pennies are in the cup?
Alexandra Reply
Uno de los ángulos suplementario es 4° más que 1/3 del otro ángulo encuentra las medidas de cada uno de los angulos
Enith Reply
June needs 48 gallons of punch for a party and has two different coolers to carry it in. The bigger cooler is five times as large as the smaller cooler. How many gallons can each cooler hold?
Alexandra Reply
I hope this is correct, x=cooler 1 5x=cooler 2 x + 5x = 48 6x=48 ×=8 gallons 5×=40 gallons
ericka
Priam has pennies and dimes in a cup holder in his car. The total value of the coins is $4.21 . The number of dimes is three less than four times the number of pennies. How many pennies and how many dimes are in the cup?
Cecilia Reply
Arnold invested $64,000 some at 5.5% interest and the rest at 9% interest how much did he invest at each rate if he received $4500 in interest in one year
Heidi Reply
List five positive thoughts you can say to yourself that will help youapproachwordproblemswith a positive attitude. You may want to copy them on a sheet of paper and put it in the front of your notebook, where you can read them often.
Elbert Reply
Avery and Caden have saved $27,000 towards a down payment on a house. They want to keep some of the money in a bank account that pays 2.4% annual interest and the rest in a stock fund that pays 7.2% annual interest. How much should they put into each account so that they earn 6% interest per year?
Leika Reply
324.00
Irene
1.2% of 27.000
Irene
i did 2.4%-7.2% i got 1.2%
Irene
I have 6% of 27000 = 1620 so we need to solve 2.4x +7.2y =1620
Catherine
I think Catherine is on the right track. Solve for x and y.
Scott
next bit : x=(1620-7.2y)/2.4 y=(1620-2.4x)/7.2 I think we can then put the expression on the right hand side of the "x=" into the second equation. 2.4x in the second equation can be rewritten as 2.4(rhs of first equation) I write this out tidy and get back to you...
Catherine
Practice Key Terms 6

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