Question

What decimal of an hour is a second ?
A.\[\;0.0002\overline 9 \]
B.\[0.00022\overline 8 \]
C.\[\;0.0002\overline 7 \]
D.\[0.0002\overline 6 \]

Answer 1

Hint: To answer this type of problem first convert one hour into a number of seconds. Then find a second that is equal to how many hours.

Complete step-by-step answer:
We all know
1 hour = 60 minutes
Similarly
1 minute = 60 seconds
Therefore
1 hour = 60 minutes⋅60 seconds / minute = 3600 seconds
We know from above that 3600 second is equal to 1 hour
So
$\Rightarrow$ 1 second\[ = \dfrac{1}{{3600\;}}\]hour =0.0002777………. hour
The 7’s continue forever.
In the above result we see that 7 is repeating
So we can write that in recurring form
Like \[\;0.0002\overline 7 \]
In this question option C is given as \[\;0.0002\overline 7 \]

So, the correct answer is “Option C”.

Note: A recurring decimal is a number which keeps repeating forever after the decimal point. The first
The recurring decimal most people meet is \[\dfrac{1}{{3\;}} \Rightarrow 0.3333......\] In most books a recurring decimal is represented by placing a dot above the number or numbers that repeat.
All recurring decimals can be represented as fractions. To find this fraction we need to generate two equations which have the same repeating part and subtracting one from the other to eliminate it.
we can round off the repeating decimal wherever you want or need; e.g., 0.00027778 hour.