Question

3. The decimal expansion of the rational number 14587 / 250 will terminate after: * *
2 points
one decimal
two decimal
three decimal
four decimal
​

Answer 1

Given:

• A number is given to us.
• The number is 14587/250.

To Find:

• The decimal expansion will end after which it will terminate.

Answer:

Given number to us is 14587/250.

It will be quite difficult for us if we divide 14587 by 250 . If we convert denominator to some numbers like 1000 or 10000 , it will be very easy for us to divide.

$\sf{=\dfrac{14587}{250}}$.

$\sf{=\dfrac{14587\times4}{250\times 4}}$

$\sf{=\dfrac{58348}{1000}}$

$\red{\bf=58.348}$

Hence the decimal will terminate after 3 places .

More to know:

A number has a terminating decimal if and only if its denominator in is in the power of $\sf{2^m\times 5^n }$

Answer 2

Answer:

The decimal expansion will terminate after 3 decimals.

Step-by-step explanation:

Given a rational number,

$\dfrac{14587}{250}$

• To convert the rational number into a decimal number, the easier way is to convert the rational number into a decimal fraction.
• Decimal fraction is the one that has the powers of 10 in the denominator namely 10, 100, 1000 etc.

In the given rational number, the denominator is 250.

And the next power of 10 to 250 is 1000.

So, to convert 250 to 1000, divide 1000 by 250,

$\dfrac{1000}{250} =4$,

therefore, the number 250 must be multiplied by 4 to get 1000.

Thus, multiplying and diving the given rational number by 250, we get

$\dfrac{14587\times 4}{250\times 4}=\dfrac{58348}{1000}$

Now there are 3 zeroes in the denominator, so from right side counting 3 digits, put the decimal point.

$\dfrac{58348}{1000}=58.348$

Hence, the decimal expansion will terminate after 3 decimals.

So, the correct answer is option 3.