Question

The decimal representation of 37/50 will * 1 point Terminate after 1 decimal place Terminate after 2 decimal place Terminate after 3 decimal place nor terminate

Answer 1

Answer:

It terminates after 2 decimal places.

Step-by-step explanation:

A rational number is said to terminate if its denominator(q) is of the form 2^m × 5^n where m and n are integers,

Here,

37/50 = p/q

So,

q = 50

Now,

50 = 2 × 5 × 5

50 = 2 × 5²

Now, we can find when the rational number terminates by looking into the powers of 2 and 5, the greatest power would give us when the rational number terminates,

Here,

q = 2¹ × 5²

Here, we have 1 and 2, the greatest power is 2, so it will terminate after 2 decimal places.

We can also check this,

37/50 = 0.74

It terminates after 2 decimal places.

Answer 2

Step-by-step explanation:

Given: 37/50

To find: Decimal expansion of given rational number

a) Terminate after 1 decimal place

b) Terminate after 2 decimal place

c) Terminate after 3 decimal place

d) Nor terminate

Solution:

We know that Decimal expansion of any rational number will be terminating only if denominator of rational number is in the form of $2^n.5^m$

where n and m are natural numbers;provided that there is no common prime factors in numerator and denominator.

Here,

37 and 50 are Co-prime numbers.

Now find the prime factors of 50.

$50 = 2 \times 5 \times 5$

Thus,

$\frac{37}{50} = \frac{37}{2 \times 5 \times 5} \\ \\ \implies \: \frac{37}{2 \times {5}^{2} } \\ \\ \implies \: \frac{37 \times 2}{ {2}^{2} \times {5}^{2} } \\ \\ \implies \: \frac{74}{( {2 \times 5)}^{2} } \\ \\ \implies \: \frac{74}{( {10)}^{2} } \\ \\ \implies \: \frac{74}{100} \\ \\ \implies0.74$

Final answer:

Decimal expansion of 37/50 terminate after 2 decimal place.

Option (b) is correct.

Hope it helps you.

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