Question

the decimal representation of 136/1400 will be ​

Answer 1

Decimal Representation

Given:

A fraction $\frac{136}{1400}$

To find:

Decimal representation of $\frac{136}{1400}$.

Explanation:

By following below steps , we can find the decimal representation of any fraction-

• Find a number which can be multiplied with denominator to make or 100, or 1000, or 1 followed by any number of zeroes.
• Multiply numerator and denominator by that number.
• Write down the numerator, putting the decimal at correct spot.

Following above steps, we get,

$=\frac{136}{14\times100}\\\\=\frac{9.71}{100}\\\\=0.0971$

Hence, 0.0971 is the correct decimal representation of  $\frac{136}{1400}$.

Answer 2

Decimal representation of 136/1400 will be ​non terminating recurring decimal .  136/1400 = $0.09\overline{714285}$

Given:

• 136/1400

To Find:

• Decimal representation type

Decimal Representation

• Any number in the form of p/q  where p and q are co primes.
• if q has only prime factors of 2 and 5 then it is terminating decimal.
• if q has prime factors other than 2 and 5 also then its non terminating recurring decimal

Step 1:

Convert 136/1400 in its simplest form

136/1400

= 68/700

= 34/350

= 17/175

Step 2:

Prime factorize Denominator 175

175 = 5 x 5 x 7

Denominator has a factor 7 which is other than 2 and 5  Hence its non terminating recurring decimal

Using long division 136/1400 = $0.09\overline{714285}$