To compare and order rational and irrational numbers, convert rational numbers to decimals and compare them directly, and for irrational numbers, compare their approximate decimal values.
Comparing and ordering rational and irrational numbers involves understanding their magnitude on the number line.
Let's compare 3 rational and irrational numbers: [tex]\( \frac{5}{3} \), \( \sqrt{2} \), and \( -\frac{4}{7} \).[/tex]
1. [tex]\( \frac{5}{3} \)[/tex] is a rational number, as it can be expressed as a fraction.
2. [tex]\( \sqrt{2} \)[/tex] is an irrational number, as it cannot be expressed as a fraction.
3. [tex]\( -\frac{4}{7} \)[/tex] is a rational number, a negative fraction.
To compare them:
1. [tex]\( \frac{5}{3} = 1.67 \)[/tex]
2. [tex]\( \sqrt{2} = 1.414 \)[/tex]
3. [tex]\( -\frac{4}{7} = -0.57 \)[/tex]
Ordering them:
[tex]\( -\frac{4}{7} < \sqrt{2} < \frac{5}{3} \)[/tex]
Calculation:
1. [tex]\( \frac{5}{3} = 1.67 \)[/tex]
2. [tex]\( \sqrt{2} = 1.414 \)[/tex]
3. [tex]\( -\frac{4}{7} = -0.57 \)[/tex]
Order: [tex]\( -\frac{4}{7} < \sqrt{2} < \frac{5}{3} \)[/tex]
So, [tex]\( -\frac{4}{7} \)[/tex] is the smallest, followed by [tex]\( \sqrt{2} \)[/tex], and [tex]\( \frac{5}{3} \)[/tex] is the largest. This is because irrational numbers lie between rational numbers and have a greater magnitude.
Complete Question:
How can you compare and order rational and irrational numbers ?
Karina earned $60 from her part time job. she spent 3/10 of it on food and 1/4 of it on music. how much money does she have left. pls show all work and answer
A volleyball curt is 61 feet lenght and 21 feet wide. How much rope will you use to mark the outline on the court?
Plz help my little sis get her hw done
in recent years 17.7% of households watched the finals of a popular reality series. There are 110.2 million households in the United States. How many households watched the finals?
In each box, 15% of the total candies are cherry flavored. In a box of 20 candies, how many are cherry flavored? Enter the missing value in the box to complete the ratio table. Part Whole 20 15 100
can someone help me I need help with this question
Lexi jarred 12 liters of jam after 4 days. How many days did Lexi spend making jam if she jarred 15 liters of jam?
(8x+1)+(4x+11)=180°
solve for x
What is 6,372,079,003 in expanded form
*I mark brainliest* Please help me on this question, explaining it, so I can understand this topic. Thank you.
what is 3/4, -7/10, -3/4, 8/10 least to greatest
how do you turn 3 7/8 into a decimal?
how do you solve
x+3/5-3x/10=7
Charles is going camping with his family their campsite is 7/8 miles away they walk at a steady speed 1 7/8 mph how many minutes will it take them to get to the campsite
A coffee pot contains 1 1/2 quarts of coffee after Tony pours an equal amount of coffee to cups 3 1/2 cups of coffee Remain the pot how much coffee did Tony pour into each cup
x = 1 1/4 cups
x = 1.25 cup
Tonya poured 1 1/4 cups into each cup.
Tony poured a total of 2 1/2 cups of coffee into an unspecified number of cups.
To solve this problem, we first need to understand the different units of measurement being used and convert them appropriately. In the United States, 1 quart is equal to 4 cups. So, we will start by converting the coffee in the pot to cups.
The coffee pot originally contained 1 1/2 quarts of coffee. To find out how much this is in cups, we multiply by 4 (since there are 4 cups in 1 quart):
1 1/2 quarts = 1.5 quarts
1.5 quarts * 4 cups/quart = 6 cups
Thus, the coffee pot had 6 cups of coffee before Tony poured it into cups.
After pouring, 3 1/2 cups of coffee remain in the pot. To find out how much coffee was poured into the cups, we subtract the remaining coffee from the initial amount:
6 cups - 3 1/2 cups = 2 1/2 cups
This means that Tony poured a total of 2 1/2 cups of coffee into the cups. If we assume that he poured an equal amount into each cup, we would divide the total amount poured by the number of cups to find the amount per cup. However, since we don't know how many cups he filled, we can only conclude that Tony poured a total of 2 1/2 cups of coffee into an unspecified number of cups.
a tin can collecting money on a store counter for the holiday season contains 15.80 dollars in quarters and dimes. if there are a total of 74 coins how many of each coins are in the tin
Final answer:
To find out how many quarters and dimes are in the tin, we set up a system of equations based on the total value and total number of coins. Solving these equations reveals that the tin contains 56 quarters and 18 dimes.
Explanation:
The student is asking for help with a system of equations problem that involves quarters and dimes that add up to $15.80, with a total of 74 coins in the tin. To solve this, we set up two equations: one for the total amount of money (1) and the other for the total number of coins (2).
Let's let Q be the number of quarters and D be the number of dimes. Therefore:
0.25Q + 0.10D = $15.80 (because quarters are $0.25 each and dimes are $0.10 each)Q + D = 74 (total number of coins)From equation (2), we can express D in terms of Q as D = 74 - Q. Substituting this into equation (1) gives us:
0.25Q + 0.10(74 - Q) = $15.80
This simplifies to:
0.25Q + 7.4 - 0.10Q = $15.80
0.15Q = $15.80 - 7.4
0.15Q = $8.40
Dividing both sides by 0.15 gives:
Q = $8.40 / 0.15
Q = 56 quarters
Substitute Q (56) back into equation (2) to find D:
D = 74 - 56
D = 18 dimes
Therefore, there are 56 quarters and 18 dimes in the tin.
what fraction part remains uncovered if 3 rectangles are covered
use the image below to help you visualize the problem.
I shaded in 3 rectangles and there are 25 rectangles in all. pls help thanks
Which of the following inequalities is not true?
-22 < 3
|-1| ≥ 0
|-9| ≠ |9|
-7 ≤ -5
help...? heres the question:
kayla says that dividing by 5/6 is the same as dividing by 5, then multiplying by 6. is she correct? why?
"Three times a number increased by eleven is seventeen" translates to which of the following equations?
11x + 3 = 17
11x - 3 = 17
3x + 11 = 17
3x - 11 = 17
What is the value of p?
0.6441−(−0.29)=p
a) 0.3541
b) 0.4541
c) 0.8341
d) 0.9341
Express -5 1/4 as a decimal
Ron used 9 centimeters of tape to wrap 3 presents. How much tape will Ron need in all if he has to wrap 5 presents?
the fastest train in the us can travel 2.6 miles per minute.At that speed how far does it go in half an hour?
1/2 + 9/10 + 4/5
A. 2 1/5
B. 2 2/10
C. 14/17
D. 22/10
Monster Mike's truck decelerates from 72 m/s to 0 m/s in 6 seconds. What is his rate of deceleration?
Answer:
this may be wrond but I think it is -12 m/s
Step-by-step explanation:
[tex]72/6=12[/tex]
The requried rate of deceleration of Monster Mike's truck is -12 m/s².
What is speed?Speed is defined as when an object is in motion, the distance covered by that object per unit of time is called speed.
Here,
The rate of deceleration of Monster Mike's truck can be calculated using the following formula,
Acceleration = (Final Velocity - Initial Velocity) / Time
Final Velocity = 0 m/s (since the truck comes to a stop)
Initial Velocity = 72 m/s
Time = 6 seconds
Substituting the given values into the formula,
Acceleration = (0 m/s - 72 m/s) / 6 s
Acceleration = -12 m/s²
Therefore, the rate of deceleration of Monster Mike's truck is -12 m/s². The negative sign indicates that the acceleration is in the opposite direction to the initial velocity of the truck.
Learn more about speed here,
https://brainly.com/question/7359669
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If a cone shaped water cup holds 23 in.³ and has a radius of 1 inch what is the height of the cup use 3.14 for pie round into the nearest hundredth
a number q multiplied by 1/4 is greater than -16
Final answer:
The student is dealing with an inequality where a number q is multiplied by [tex]\frac{1}{4}[/tex] and needs to be greater than -16. Upon solving, the result is that q must be greater than -64.
Explanation:
The student is asking about an inequality in mathematics where a number q multiplied by [tex]\frac{1}{4}[/tex] must be greater than -16. To solve this, we set up the inequality as follows:
[tex]\frac{1}{4}[/tex] × q > -16
When solving for q, you would multiply both sides of the inequality by 4 to isolate q:
q > -16 × 4
q > -64
Therefore, the value of q must be greater than -64 to satisfy the inequality.
Noya needs to determine the number of books that will fit into a box. If the box has a length of 18 inches and each book is 2/9 of an inch thick, which expression can be used to determine the number of books that will fit into the box?
A Cab charges $1.75 for the flat fee and $0.25 for each mile. Write and solve an inequality to determine how many miles Eddies can travel if he has $15 to spend