Test: Rational Numbers - Class 9 MCQ

To find the product of 7/8 and -4/21, follow these steps:

• Multiply the numerators: 7 × -4 = -28.
• Multiply the denominators: 8 × 21 = 168.
• Combine the results: -28/168.
• Simplify the fraction: -28/168 can be reduced to -1/6.

The final answer is -1/6.

 5 / (3 + √8)  x  ( (3 - √8) /  (3 - √8)

=  5 ( 3 - √8)/(3^{2 -} 8 ⁾

= 5 ( 3 - √8 ) / 9 - 8  = 15 - 5√8 

So option C is correct. 

To express 2.2323... as a fraction, follow these steps:

• Let x = 2.2323...
• The repeating part is 23, so multiply by 100 to shift the decimal: 100x = 223.2323...
• Subtract the original equation from this: 100x - x = 223.2323... - 2.2323...
• This simplifies to: 99x = 221
• Divide both sides by 99: x = 221/99

Therefore, the fraction form of 2.2323... is 221/99.

Remember the general formula to find rational number between two

given number 1/2(a+b)[where a, b are given numbers]

A rational number between 1 and 2 is 1/2(1+2)=3/2

Let the three digit number be 439
The sum of digits =16
Difference =439−16=423 which is divisible by 9.

Any negative number that is greater than -1 but less than 0 falls within the specified range. So the correct answer is C. 

Given mixed fraction:
 (which means 5 + 2/3)

Step 1: Convert the mixed fraction to an improper fraction
 = (5 × 3 + 2) / 3 = (15 + 2) / 3 = 17/3

Step 2: Convert 17/3 to a decimal
Divide 17 by 3:
17 ÷ 3 = 5.666… (where 6 keeps repeating)

So, 17/3 = 5.666…
This means the digit 6 repeats forever.

Analyze the Decimal:
The decimal 5.666… does not end (it goes on forever).
It is recurring because the digit 6 keeps repeating in a pattern.

Match with the Options:

• a) a terminating decimal — Incorrect. A terminating decimal ends after some digits, like 0.75. Here, 5.666… continues forever.

• b) a non-terminating recurring decimal — Correct. 5.666… is non-terminating (it doesn’t end) and recurring (the digit 6 repeats).

• c) a non-terminating non-recurring decimal — Incorrect. A non-recurring decimal has no pattern, like pi (3.14159…). Here, we see the digit 6 repeating.

• d) an integer — Incorrect. 5.666… is not a whole number. An integer would be 5 or 6.

Extra Tip:
A fraction will have a terminating decimal only if the denominator (after simplification) has only the numbers 2 and/or 5 as prime factors.
Here, the denominator is 3, which is not 2 or 5. So, the decimal cannot terminate; it must be recurring.

Final Answer: (b) a non-terminating recurring decimal.

A rational number is a number that is in the form of p/q, where p and q are integers, and q is not equal to 0

Step 1: Multiply the numerators
Multiply 7 and -4:
7 × -4 = -28

Step 2: Multiply the denominators
Multiply 8 and 21:
8 × 21 = 168

So, the product is:
-28/168

Step 3: Simplify the fraction
Find the greatest common factor of 28 and 168, which is 28.

Divide both the numerator and denominator by 28:
-28 ÷ 28 = -1
168 ÷ 28 = 6

So, -28/168 simplifies to -1/6

To determine if two numbers are co-prime, we check if their greatest common divisor (GCD) is 1.

• 2 and 3: HCF is 1. They are co-prime.


• 2 and 4: HCF is 2. They are not co-prime.


• 2 and 6: HCF is 2. They are not co-prime.


• 2 and 110: HCF is 2. They are not co-prime.


 

Therefore, the correct answer is A: 2, 3.

The rational numbers include all the integers, plus all fractions, or terminating decimals and repeating decimals. Every rational number can be written as a fraction a/b, where aand b are integers. For example, 3 can be written as 3/1, -0.175 can be written as -7/40, and 1 1/6 can be written as 7/6. All natural numbers, whole numbers, and integers are rationals, but not all rational numbers are natural numbers, whole numbers, or integers.

Let x = 0.234234234.........
(1) Then , multiply both side with 1000 1000x = 234.234234......(2) Now Eq.(2)-(1) 1000x-x = 234.234234- 0.234234 999x = 234 x = 234/999

There is no single number between 3 and 4, there is an infinite amount of numbers. If you are asking for INTEGERS, there are none. If not, you can have unlimited numbers between 3 and 4. For example, a number could be 3.0000000000000000005 or 3.9999999999999997.

X=0.230769 (1)

Multiply bot sides by 1000000, we get 1000000x = 230769.230769 (2)

subtracting (1) from (2), we get

230769 =999999x then, x = 230769/999999 =3/13

Real numbers are the numbers that can be placed on number line
And rational number can be placed on number line so all rational numbers are real number.

As in the given term x=32, 32 is recurring, so to get value in fraction, we will multiply both sides by 100 to get 32 before decimal for subtraction and cancel the recurring term after decimal

5/13 = 0.384615……,    - (1)

We know that 10/13 = 2* (5/13)
So, to find 10/13
just multiply equation (1) by 2 

2 * (5/13) = 2 * 0.384615
10/13 = 0.769230

- 5 / 4 + x = -1

x = -1 + 5 / 4

x = (-4 + 5) / 4

x = 1 / 4