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Maths-

General

Easy

Question

Find the equivalent fraction for the following decimal number 0.57894736842 and say whether it is a rational number or an irrational number?

hint Hint:

Hint:
A rational number is a type of real number, which is in the form of p/q where q is not equal to zero. For a decimal number, if a decimal expansion is a terminating decimal then it is a rational number and if a decimal expansion is non-terminating but a repeating decimal then it is also a rational number but if a decimal expansion is a non-repeating and non-terminating decimal then it is an irrational number.

The correct answer is: rational number and its equivalent fraction is 28947368421/50000000000.

As 0.57894736842 is a terminating decimal so it can be expressed as p/q form.
Step 1 of 2:
Write down 0.57894736842 divided by 1:
$equals fraction numerator 0.57894736842 over denominator 1 end fraction$
=
Step 2 of 2:
Multiplying numerator and denominator by 1011(because there are 11 digits after the decimal point)
$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell equals fraction numerator 0.57894736842 cross times 10 to the power of 11 over denominator 1 cross times 10 to the power of 11 end fraction end cell row cell equals 57894736842 over 10 to the power of 11 end cell end table$
Simplifying the fraction:
$equals 28947368421 over 50000000000$
Final Answer:
Hence, 0.57894736842 is a rational number and its equivalent fraction is $equals 28947368421 over 50000000000$

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