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Answers
1.d
2.c
3.b
4.b
5.d
6.b
7.a
8.b
9.a
10.a
Step-by-step explanation:
Solutions:-
1) Given number = 3/40
=> 3/(2×2×2×5)
=> 3/(2³×5)
On multiplying both numerator and the denominator with 5²
=> (3/2³×5)×(5²/5²)
=> (3×5²)/(2³×5³)
=> (3×25)/(10³
=> 75/10³
=> 75/1000
=> 0.075
3/40 = 0.075
2)
Given numbers = 3 and 4
We know that
The rational number between a and b is (a+b)/2
Mean method
Let a = 3 and b = 4
The rational number between 3 and 4
=> (3+4)/2
=> 7/2
The rational number between 3 and 4 = 7/2
3)
Given numbers = 3/5 and 4/5
The rational number between them by mean method
=> [(3/5)+(4/5)]/2
=> [(3+4)/5]/2
=> (7/5)/2
=> 7/(5×2)
=> 7/10
The rational number between 3/5 and 4/5 = 7/10
4)
Given numbers = 1/2 and 3/4
The rational number between them by mean method
=> [(1/2)+(3/4)]/2
=> [(2+3)/4]/2
=> (5/4)/2
=> 5/(4×2)
=> 5/8
The rational number between 1/2 and 3/4 = 5/8
5)
√-16 is not a rational number
It is an imaginary number
√-16 = √(-(4×4)) = 4√-1 = 4√i² = 4i
Since i² = -1
6)
3√8 is an irrational number
because 3√8 can be written as
=> 3×√(2×2×2)
=> 3×2√2
=> 6√2
=> the product of a rational number and an irrational number is always an irrational number.
7)Given number = 1/5
On multiplying both numerator and the denominator with 2
=> (1/5)×(2/2)
=> (1×2)/(5×2)
=> 2/10
=> 0.2
8)Given number = 3 3/8
=> [(3×8)+3]/8
=> (24+3)/8
=> 27/8
=> 27/2³
On multiplying both numerator and the denominator with 5³
=> (27/2³)×(5³/5³)
=> (27×5³)/(2³×5³)
=> (27×125)/(10³)
=> 3375/1000
=> 3.375
3 3/8 = 3.375
9) Given number = 5/6
6)50(0.8333...
48
____
20
18
____
. 20
18
____
2
____
5/6 = 0.83 bar on 3
10)Given number = 8/27
27 ) 80 ( 0.29629...
54
____
260
243
_____
170
162
______
80
54
_____
260
243
_______
. 17
_________
8/27 = 0.296 bar on 296
Used formulae:-
- In a rational number the denominator is in the form of 2^m × 5^n then it is a terminating decimal.
- To convert a rational number into decimal number we use division .
Answer:
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