A rational number p/q has a terminating decimal expansion if and only if the prime factorization of its denominator q (after simplify the fraction) contains only the prime factorization of its denominator q (after simplifying the fraction) contains only the prime factor 2 and/or 5. (a). 2 or 5 IfRead more
A rational number p/q has a terminating decimal expansion if and only if the prime factorization of its denominator q (after simplify the fraction) contains only the prime factorization of its denominator q (after simplifying the fraction) contains only the prime factor 2 and/or 5.
(a). 2 or 5
If the denominator has only 2, and 5, or both(e.g., 10, 20, 25, etc.), the decimal expansion terminates.
(b). 3 or 5
The presence of 3 in the denominator(e.g., 1/3 = 0.3333…) causes a non-terminating repeating decimal.
(c). 9 or 11
9 = 3³ and 11 are not factors that produce a terminating decimal.
(d) 3 or 7
Both 3 and 7 cause non-terminating repeating decimals.
This question related to Chapter 1 Mathematics Class 9th NCERT. From the Chapter 1 Number System. Give answer according to your understanding.
Let's analyze each statement carefully: Option (a): Every whole number is a natural number Natural numbers (N): {1,2, 3, 4,...} Whole numbers (W): {0,1,2,3,4,...} Since whole number include 0, but natural number do not, this statement is false. Option (b): Every integer is a rational number IntegersRead more
Let’s analyze each statement carefully:
Option (a): Every whole number is a natural number
Natural numbers (N): {1,2, 3, 4,…}
Whole numbers (W): {0,1,2,3,4,…}
Since whole number include 0, but natural number do not, this statement is false.
Option (b): Every integer is a rational number
Integers (Z): {…, -3, -2, -1, 0, 1,2,3,…)
Rotational number (Q): Numbers that can be expressed as p/q, where p and q are integers, and q ≠ 0.
Every integer x can be written as x/1, which is in the form of a rotational number.
Thus this statement is true.
Option (c): Every rational number is an integer.
Example 1/2 is a rational number but not an integer.
So, this statement is false.
Option (d): Every integer is a whole number
Whole number do not include negative numbers, but integers do.
Example: -1 is an integer but not a whole number.
Thus, this statement is false.
Final Answer: The correct answer is (b) Every integer is a rotational number. This question related to Chapter 1 Mathematics Class 9th NCERT. From the Chapter 1 Number System. Give answer according to your understanding.
We are given that m and n are two natural numbers, and mⁿ = 32 We need to find the value of nᵐⁿ. Step 1: Find Possible Value of m and n Since 32 and 2⁵, we look for natural numbers m and n such that: mⁿ = 32 Possible values are: m = 2, n = 5( since 2⁵ = 32) Step 2: Compute nᵐⁿ We substitute n = 5Read more
We are given that m and n are two natural numbers, and mⁿ = 32
We need to find the value of nᵐⁿ.
Step 1: Find Possible Value of m and n
Since 32 and 2⁵, we look for natural numbers m and n such that: mⁿ = 32
Possible values are:
m = 2, n = 5( since 2⁵ = 32)
Step 2: Compute nᵐⁿ
We substitute n = 5 and mⁿ = 32:
nᵐⁿ = 5³²
Step 3: Identify the correct option
None of the options match 5³² directly.
Please verify if there was a misinterpretation in the problem statement or options. If you meant nᵐ*ⁿ instead of nᵐⁿ , let’s check:
nᵐ*ⁿ = 5²×⁵ = 5¹⁰
This matches option (c) 5¹⁰.
This question related to Chapter 1 Mathematics Class 9th NCERT. From the Chapter 1 Number System. Give answer according to your understanding.
We need to find a rational number between 3/5 and 4/5 fom the given options. Step 1: Convert to Decimal Form 3/5 = 0.6 4/5 = 0.8 Now, we check which given options lie in the range (0.6, 0.8). Step 2: Convert the Options to Decimal Form (a). 7/5 = 1.4 (Not between 0.6 and 0.8) (b). 7/10 = 0.7 (BetwRead more
We need to find a rational number between 3/5 and 4/5 fom the given options.
Step 1: Convert to Decimal Form
3/5 = 0.6
4/5 = 0.8
Now, we check which given options lie in the range (0.6, 0.8).
Step 2: Convert the Options to Decimal Form
(a). 7/5 = 1.4 (Not between 0.6 and 0.8)
(b). 7/10 = 0.7 (Between 0.6 and 0.8)
(c). 3/10 = 0.3 (Less than 0.6)
(d). 4/10 = 0.4 ( Less than 0.6)
Conclusion: The only rational number between 3/5 and 4/5 is 7/10 (option b).
This question related to Chapter 1 Mathematics Class 9th NCERT. From the Chapter 1 Number System. Give answer according to your understanding.
To find a rational number between 3 and 4, we need to check which of the given options lies in the interval (3,4)(3,4)(3,4). Checking each option: (a). 3/2 =1.5, 1.5 is less than 3, so it is not between 3 and 4. (b). 4/3 ≈ 1.33, 1.33 is also less than 3, so it is not between 3 and 4. (c). 7/2 = 3.5,Read more
To find a rational number between 3 and 4, we need to check which of the given options lies in the interval (3,4)(3,4)(3,4).
Checking each option:
(a). 3/2 =1.5, 1.5 is less than 3, so it is not between 3 and 4.
(b). 4/3 ≈ 1.33, 1.33 is also less than 3, so it is not between 3 and 4.
(c). 7/2 = 3.5, 3.5 is between 3 and 4, so this is a valid option.
(d). 7/4 = 1.75, 1.75 is less than 3, so it is not between 3 and 4.
Conclusion:
The only rational number in the given options that lies between 3 and 4 is 7/2 (option c).
This question related to Chapter 1 Mathematics Class 9th NCERT. From the Chapter 1 Number System. Give answer according to your understanding.
Decimal expansion of a rational number is terminating if in its denominator there is:
A rational number p/q has a terminating decimal expansion if and only if the prime factorization of its denominator q (after simplify the fraction) contains only the prime factorization of its denominator q (after simplifying the fraction) contains only the prime factor 2 and/or 5. (a). 2 or 5 IfRead more
A rational number p/q has a terminating decimal expansion if and only if the prime factorization of its denominator q (after simplify the fraction) contains only the prime factorization of its denominator q (after simplifying the fraction) contains only the prime factor 2 and/or 5.
(a). 2 or 5
If the denominator has only 2, and 5, or both(e.g., 10, 20, 25, etc.), the decimal expansion terminates.
(b). 3 or 5
The presence of 3 in the denominator(e.g., 1/3 = 0.3333…) causes a non-terminating repeating decimal.
(c). 9 or 11
9 = 3³ and 11 are not factors that produce a terminating decimal.
(d) 3 or 7
Both 3 and 7 cause non-terminating repeating decimals.
This question related to Chapter 1 Mathematics Class 9th NCERT. From the Chapter 1 Number System. Give answer according to your understanding.
For more please visit here:
See lesshttps://www.tiwariacademy.in/ncert-solutions/class-9/maths/
Which of the following is true?
Let's analyze each statement carefully: Option (a): Every whole number is a natural number Natural numbers (N): {1,2, 3, 4,...} Whole numbers (W): {0,1,2,3,4,...} Since whole number include 0, but natural number do not, this statement is false. Option (b): Every integer is a rational number IntegersRead more
Let’s analyze each statement carefully:
Option (a): Every whole number is a natural number
Natural numbers (N): {1,2, 3, 4,…}
Whole numbers (W): {0,1,2,3,4,…}
Since whole number include 0, but natural number do not, this statement is false.
Option (b): Every integer is a rational number
Integers (Z): {…, -3, -2, -1, 0, 1,2,3,…)
Rotational number (Q): Numbers that can be expressed as p/q, where p and q are integers, and q ≠ 0.
Every integer x can be written as x/1, which is in the form of a rotational number.
Thus this statement is true.
Option (c): Every rational number is an integer.
Example 1/2 is a rational number but not an integer.
So, this statement is false.
Option (d): Every integer is a whole number
Whole number do not include negative numbers, but integers do.
Example: -1 is an integer but not a whole number.
Thus, this statement is false.
Final Answer: The correct answer is (b) Every integer is a rotational number. This question related to Chapter 1 Mathematics Class 9th NCERT. From the Chapter 1 Number System. Give answer according to your understanding.
For more please visit here:
See lesshttps://www.tiwariacademy.in/ncert-solutions/class-9/maths/
If m and n are two natural numbers and mⁿ = 32, then nᵐⁿ is
We are given that m and n are two natural numbers, and mⁿ = 32 We need to find the value of nᵐⁿ. Step 1: Find Possible Value of m and n Since 32 and 2⁵, we look for natural numbers m and n such that: mⁿ = 32 Possible values are: m = 2, n = 5( since 2⁵ = 32) Step 2: Compute nᵐⁿ We substitute n = 5Read more
We are given that m and n are two natural numbers, and mⁿ = 32
We need to find the value of nᵐⁿ.
Step 1: Find Possible Value of m and n
Since 32 and 2⁵, we look for natural numbers m and n such that: mⁿ = 32
Possible values are:
m = 2, n = 5( since 2⁵ = 32)
Step 2: Compute nᵐⁿ
We substitute n = 5 and mⁿ = 32:
nᵐⁿ = 5³²
Step 3: Identify the correct option
None of the options match 5³² directly.
Please verify if there was a misinterpretation in the problem statement or options. If you meant nᵐ*ⁿ instead of nᵐⁿ , let’s check:
nᵐ*ⁿ = 5²×⁵ = 5¹⁰
This matches option (c) 5¹⁰.
This question related to Chapter 1 Mathematics Class 9th NCERT. From the Chapter 1 Number System. Give answer according to your understanding.
For more please visit here:
See lesshttps://www.tiwariacademy.in/ncert-solutions/class-9/maths/
A rational number between 3/5 and 4/5 is:
We need to find a rational number between 3/5 and 4/5 fom the given options. Step 1: Convert to Decimal Form 3/5 = 0.6 4/5 = 0.8 Now, we check which given options lie in the range (0.6, 0.8). Step 2: Convert the Options to Decimal Form (a). 7/5 = 1.4 (Not between 0.6 and 0.8) (b). 7/10 = 0.7 (BetwRead more
We need to find a rational number between 3/5 and 4/5 fom the given options.
Step 1: Convert to Decimal Form
3/5 = 0.6
4/5 = 0.8
Now, we check which given options lie in the range (0.6, 0.8).
Step 2: Convert the Options to Decimal Form
(a). 7/5 = 1.4 (Not between 0.6 and 0.8)
(b). 7/10 = 0.7 (Between 0.6 and 0.8)
(c). 3/10 = 0.3 (Less than 0.6)
(d). 4/10 = 0.4 ( Less than 0.6)
Conclusion: The only rational number between 3/5 and 4/5 is 7/10 (option b).
This question related to Chapter 1 Mathematics Class 9th NCERT. From the Chapter 1 Number System. Give answer according to your understanding.
For more please visit here:
See lesshttps://www.tiwariacademy.in/ncert-solutions/class-9/maths/
A rational number between 3 and 4 is:
To find a rational number between 3 and 4, we need to check which of the given options lies in the interval (3,4)(3,4)(3,4). Checking each option: (a). 3/2 =1.5, 1.5 is less than 3, so it is not between 3 and 4. (b). 4/3 ≈ 1.33, 1.33 is also less than 3, so it is not between 3 and 4. (c). 7/2 = 3.5,Read more
To find a rational number between 3 and 4, we need to check which of the given options lies in the interval (3,4)(3,4)(3,4).
Checking each option:
(a). 3/2 =1.5, 1.5 is less than 3, so it is not between 3 and 4.
(b). 4/3 ≈ 1.33, 1.33 is also less than 3, so it is not between 3 and 4.
(c). 7/2 = 3.5, 3.5 is between 3 and 4, so this is a valid option.
(d). 7/4 = 1.75, 1.75 is less than 3, so it is not between 3 and 4.
Conclusion:
The only rational number in the given options that lies between 3 and 4 is 7/2 (option c).
This question related to Chapter 1 Mathematics Class 9th NCERT. From the Chapter 1 Number System. Give answer according to your understanding.
For more please visit here:
See lesshttps://www.tiwariacademy.in/ncert-solutions/class-9/maths/