Question

12. After how many places decimal places will the decimal expansion of the rational
number 359 / 2^6 x 5^3 terminate?​

Answer 1

Answer:

after 2 places from my views

Answer 2

Answer:

The rational number  $\frac{359}{2^6 5^3}$ terminates in 6 places of decimal.

Step-by-step explanation:

Required to find,

The number of decimal places in which the rational number  $\frac{359}{2^6 5^3}$terminates

Recall the concept

A rational number in its simplest form $\frac{p}{q}$ is a terminating decimal if q is of the form $2^mX 5^n$,  for any non-negative integers 'm' and 'n'

Solution:

The rational number given,  is  $\frac{359}{2^6 5^3}$, this rational number is in its simplest form.

Since the denominator is of the form $2^mX 5^n$, then the given rational number is a terminating decimal.

Multiply both numerator and denominator by $5^3$ we get,

$\frac{359}{2^6 5^3} = \frac{359X 5^3}{2^6 5^3 X5^3} = \frac{359X125}{2^6 5^6}$

$= \frac{44875}{(2X 5)^6}$

$= \frac{44875}{(10)^6}$

= 0.044875

∴ The rational number  $\frac{359}{2^6 5^3}$ terminates in 6 places of decimal.

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