Example
indeterminate
Your Turn
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Today’s Topic
Fun Fact
Let’s start the chapter with a fun fact.
1.5 is rational,
because it can be written as
because it can be written as
]]>
0.666666 .... is rational, Why?
Because it can be written as
]]>
Caution: The denominator cannot equal to zero.]]>
π is irrational, why?
Because it cannot be written as fraction
π =3.1415926535897932384626433832795 (and more).
The popular approximation of π =
=3.1428571428571 (and more) is closed but not accurate (as you can see from above).
]]>
]]>
Many square root & cube roots are also irrational number.
√3 = 1.7320508075688772935274463415059 (and more)
3√ 5 = 1.70997594668 (and more)
√4 = 2 (rational), √9 = 3 (rational) & 3√ 5 = 1.70997594668 (irrational)
]]>
(rational), √9 = 3 (rational) & 3√ 5 = 3 (rational)]]>
= 0.2
]]>
= 0.625
]]>
= 0.3333 (repeating decimal)
]]>
= 0.363636 (repeating decimal)
]]>
What are the characteristics of irrational number?]]>
Relationship between different sets of numbers.
Let’s see which sets of number are rational & which sets of number are irrational. Firstly , let’s look at different sets of number.]]>
Natural numbers (also known as counting numbers) are the numbers that we use to count. It starts with 1, followed by 2, then 3, and so on.
In set notation: Natural Numbers (N) = { 1, 2 3, ……….}]]>
Whole numbers are a slight "upgrade" of the natural numbers because we simply add the element "zero" to the current set of natural numbers. Think of whole numbers as natural numbers together with zero.
In set notation: Whole Numbers (W) = { 0,1, 2 3, ……….}]]>
The integers include all whole numbers together with the "negatives" of the natural numbers.
In set notation: Integers (W) = { …….,-3,-2,-1,0,1, 2 3, ……….}]]>
Includes natural numbers, whole numbers & integers.]]>
All numbers except for rational numbers. ]]>
The real numbers includes both the rational and irrational numbers. Remember that under the rational number, we have the subcategories of integers, whole numbers and natural numbers.]]>
Simple Interest : Amount
So, at the end when it’s time to pay back the money. I just pay the Interest
amount.]]>
In Formula,
Amount = Principal + Interest ]]>
Let's solve problem together and use the above formula.
Simple Interest: Amount Example
Example
Rasna borrowed Rs. 2,000 from Nabil Bank . Find the Amount if Rasna paid interest of Rs 500.
Solution:
Given,
Principal (P) = Rs. 2,000
Interest (I) = Rs. 500
Now, using formula
Amount = Principal+ Interest
= 2000 + 500
= Rs. 2,500
∴ Amount paid by Rasna is Rs. 2,500
You can also use Amount formula to find Principal& Interest.
]]>
Interest ( I ) = Rs 500
Now, Using Formula
Amount = Principal+ Interest
= 2000 + 500
= Rs 2,500
Amount (A) = Principal (P) + Interest (I)
or, A = P + I
or, A = P +
[Replacing value of I =
]
or, A =
or, 100 A = P ( 100 + TR)
∴ P =
You can use the above formula to find Principal (P), Amount (A), Time (T) & Rate (R)
Let's solve a problem together and use the above formula.
]]>
(Replacing value of I = ( P X T X R)/100)]]>
Simple Interest:Example
Example 4
Solution :
Given,
Principal (P) = ?
Rate of interest (R) = 8%
Time (T) = 5 Years
Amount (A) = Rs. 11,200
Now, using formula
P =
=
=
= Rs. 8,000
∴ Hari initially Borrowed Rs. 8,000 from Ram.
]]>
Principal (P) = ?
Rate of interest (R) = 8%
Time (T) = 5 Years
Amount (A) = Rs 11,200
Now, Using Formula
P = (A X 100)/100 + TR
= (11200 X 100)/100 + 5 X 8
= 1120000/140
= Rs 8,000
∴ Hari initially Borrowed Rs 8,000 from Ram
16days
Rational
Irrational
Are you ready to identify rational and irrational numbers?
7/8
1/3
2√3
0.97
√1.6
-√8
0.3030030003...
√9
π
8/2
0
-√11
√2/5
√16/9
-3
Congratulations! You played well.
Identify between rational and irrational numbers and click on the correct sack.
Is the statement True or False?
Hello, I am OLE rhino. I am taking part in running competition. Help me to win this competition. You have to answer the questions that are asked, correctly. Only then, I will get to run. I will only win if you answer all the questions correctly.
Come Let's play.
RULE 1: EXERCISES : click on the correct answer
Hurray! We won.
Its okay, we were playing good.
Why didn't you give me chance to run?
Our practice is not enough, do you understand?
We have to practice a lot, then victory is ours.
RULE 2: EXERCISES : click on the correct answer
RULE 3: EXERCISES : click on the correct answer
RULE 4: EXERCISES : click on the correct answer
COMBINED EXERCISES – VERY DIFFICULT
Score:
Total Problems:
A natural number is also a whole number.
True
False
Any integer is a whole number.
Every rational number is also an integer.
Every integer is a rational number.
Every natural number is a whole number, integer, and a rational number.
Every whole number is a natural number, integer, and a rational number.
The set of whole numbers includes the number zero and all natural numbers. This is a true statement.
The set of integers is composed of the number zero, natural numbers, and the "negatives" of natural numbers. That means some integers are whole numbers, but not all. For instance, −2 is an integer but not a whole number. This statement is false.
The word "every" means "all". Can you think of a rational number that is not an integer? You only need one counter example to show that this statement is false. The fraction is an example of a rational number but not an integer. So this statement is false.
This is true because every integer can be written as a fraction with a denominator of 1.
Natural numbers are found within the sets of whole numbers, integers, and rational numbers. That makes it a true statement.
It is a false statement since whole numbers belong to the sets of integers and rational numbers, but not to the set of natural numbers.
Congratulations!!
You have completed this exercise.
You scored #userscore# out of #totalscore#.
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Quiz Summary
Correct Answer
Drag and drop the numbers to the appropriate box
0.75
0.005
0.5444
√7
0.1414
√25
Need1
Need2
Need3
Want1
Want2
Want3