Question

The decimal representation of the rational number 21/16 is ​

Answer 1

Answer:

1.3125

Step-by-step explanation:

The formula: Divide p by q (p/q, the rational number itself)

Here, it is 21/16, which gives the answer as 1.3125.

Answer 2

Given : 21 /16

$\dfrac{21}{16 }$

To Find : Decimal Expansion type

Solution:

$\dfrac{21}{16 }$

21 = 3 * 7

16 = 2 * 2 * 2 * 2

$=\dfrac{3 \times 7 }{2 \times 2 \times 2\times 2}$

$=\dfrac{3 \times 7}{2^4 \times 5^0}$

As denominator is of the form 2ᵃ*5ᵇ   where a and b are whole numbers ( non negative integers)

so Decimal expansion will be Terminating

$=\dfrac{3 \times 7 \times 5^4}{2^4 \times 5^0 \times 5^4}$

= 13125/10000

= 1.3125

               1.3125    

       16  _|  21.0000   |_

                  16

               ____

                   50

                   48

                ____

                   20

                   16

                  ____

                   40

                    32

                    _____

                       80

                       80

                       ____

                         0

Decimal expansion will be Terminating

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