Which of the following is the 21st digit to the right of the decimal

Question

Which of the following is the 21st digit to the right of the decimal place in the decimal expression of 5/22?

A. 1
B. 2
C. 5
D. 7
E. 11

tu2325 · Answer

For such type of question we should start dividing and try to see if a pattern emerges (which usually does).

Now, when we reach the third decimal place we notice that after that it starts repeating.

That is 5/22 = 0.2272727... So except the first decimal place there is repeating pattern. Hence, the 21st digit to the right will be 7.

Thus, the correct option is D.

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MvArrow · Answer

How I am supposed to convert 5/22 into a decimal form without a calculator?

niks18 · Answer

HI  MvArrow ,

\frac{5}{22} = \frac{5}{2*11}=\frac{2.5}{11} , division by 11 should not be a challenge even without calculator.

Phlopp · Answer

When confronted with such a division, proceed as follows:

5/22 = 0 Remainder 5 => What we know: 5/22=0,...
Now add a 0 to the Remainder and determine the first decimal digit.
50/22 = 2 Remainder 6 => 5/22=0,2...
Add a 0 to the Remainder again and determine the second decimal digit.
60/22 = 2 Remainder 16 => 5/22=0,22...
Add a 0 to the Remainder again and determine the second decimal digit.
160/22 = 7 Remainder 6 => 5/22=0,227...

You might have noticed that we already got a remainder of 6 when determining the first decimal digit. And from that 6, which turned into a 60, we got a remainder of 16 which in turn returned a remainder of 6. So the pattern is going to repeat forever and we can conclude that 5/22 = 0,2 ̅27 meaning 27 will repeat forever.

The third digit after the comma is a 7 so the 21st is also gonna be a 7 because it's also odd. 
Answer D

Which of the following is the 21st digit to the right of the decimal

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GMAT Problem Solving (PS) Questions

Which of the following is the 21st digit to the right of the decimal

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