Question

*Decimal expansion of 15/35 will be*

1️⃣ Terminating
2️⃣ Non Terminating
3️⃣ Non Terminating repeating
4️⃣ None of these​

Answer 1

Given :- Decimal expansion of 15/35 will be ?

1️⃣ Terminating

2️⃣ Non Terminating

3️⃣ Non Terminating repeating

4️⃣ None of these

Answer :-

we know that, in a decimal expansion while checking the prime factors of denominator ,

• if prime factor are 2, or 5 , or 2 and 5 both . Than the given fraction is a terminating decimal expansion .
• if prime factors are other than 2 or 5 , than the given fraction is a non - terminating decimal expansion .

so,

→ 15/35

→ 5*3/5*7

→ 3/7

now, checking the prime factors of denominator we get,

→ Denominator = 7

→ Prime factors of denominator = 1 * 7

→ 7 is other than 2 or 5 .

therefore, we can conclude that, decimal expansion of 15/35 will be non - terminating . (Option 2 is correct answer. )

Learn more :-

https://brainly.in/question/39499253

Answer 2

SOLUTION

TO CHOOSE THE CORRECT OPTION

Decimal expansion of 15/35 will be

1. Terminating

2. Non Terminating

3. Non Terminating repeating

4. None of these

CONCEPT TO BE IMPLEMENTED

$\displaystyle\sf{Fraction = \frac{Numerator}{Denominator} }$

A fraction is said to be terminating if prime factorisation of the denominator contains only prime factors 2 and 5

If the denominator is of the form

$\sf{Denominator = {2}^{m} \times {5}^{n} }$

Then the fraction terminates after N decimal places

Where N = max { m , n }

EVALUATION

Here the given fraction is

$\displaystyle\sf{ \frac{15}{35} }$

Now this fraction can be rewritten as

$\displaystyle\sf{ \frac{15}{35} }$

$\displaystyle\sf{ = \frac{3}{7} }$

Here the denominator = 7

Now the prime factorisation of the denominator contains only 7 as a prime factor

So the decimal expansion is non terminating

FINAL ANSWER

Hence the correct option is 2. Non Terminating

━━━━━━━━━━━━━━━━

Learn more from Brainly :-

1. The decimal expansion of 49/2³5³

contains six digits after the decimal point.

https://brainly.in/question/36368731

2. Without actually dividing find which of the following are terminating decimals.

i. 3/25 ii. 11/18 iii. 13/20 iv. 41/42

https://brainly.in/question/135746

3. without actually performing the long division state whether 13/3125 and 13/343 will have a terminating decimal expansion...

https://brainly.in/question/23797327