Question

convert the following rational numbers into decimal form 17/6,20/7​

Answer 1

Given data: The rational numbers $\frac{17}{6},\frac{20}{7}$.

To Find: The decimal form of the rational numbers $\frac{17}{6},\frac{20}{7}$

Solution:

Rational number consists of numerator and denominator.

To convert the rational number into decimal form, divide the numerator and denominator.

Consider the rational number $\frac{17}{6}$,

Here, 17 is the numerator and 6 is the denominator.

Divide the numerator and denominator,

$=\frac{17}{6}$

$=2.83$

Hence, the decimal form of $\frac{17}{6}$ is $2.83$

Consider the rational number $\frac{20}{7}$,

Here, 20 is the numerator and 7 is the denominator.

Divide the numerator and denominator,

$=\frac{20}{7}$

$=2.86$

Hence, the decimal form of $\frac{20}{7}$ is $2.86$

Therefore, the decimal form of the rational numbers $\frac{17}{6}$ and $\frac{20}{7}$ is $2.83$ and $2.86$ respectively.

Answer 2

17/6 =  $2.8\overline{3}$  non terminating recurring decimal

20/7 =  $2.\overline{857142}$

Given:

• Rational Numbers
• 17/6
• 20/7

To Find:

• Convert in Decimal form

Rational Numbers

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

Rational numbers are terminating decimals or non terminating recurring decimal.

17/6  

Denominator has factor 2 and 3  hence its  non terminating recurring decimal.

Use Long Division

      2.833

6  )  17.000  (

      12

    ____

      50

      48

     ____

      20

       18

     ___

         20

          18

        ____

           2

As remainder is repeating hence 3 will be recurring

so 17/6 = 2.833...  =   $2.8\overline{3}$

Using similar method for 20/7

20/7 =  $2.\overline{857142}$