Question

Express 5381 in powers of nine.

Answer 1

Hint: Here we will divide the given number by nine until the quotient obtained is zero and note the remainders in each case and then write all the remainders together to get the desired answer.

Complete step by step answer:
The given number is 5381.
Now we know that in order to express this number in powers of nine we need to divide the given number by nine until the quotient obtained is zero and note the remainders in each case.
Hence, dividing 5381 by 9 we get:-
     \[\underline {{\text{ }}} \]
\[9)5381(597\]
\[\underline { - 5373} \]
  \[{\text{8}}\]
Here, the quotient is 597 and the remainder if 8……………… (1)
Now since the quotient is not equal to zero therefore, we again need to divide the resulting quotient by 9.
Hence on dividing we get:-
    \[\underline {{\text{ }}} \]
\[9)597(66\]
 \[\underline { - 544} \]
   \[3\]
Here, the quotient is 66 and the remainder is 3…………………….. (2)
Now since the quotient is not equal to zero therefore, we again need to divide the resulting quotient by 9.
Hence on dividing we get:-
   \[\underline {{\text{ }}} \]
\[9)66(7\]
\[\underline { - 63} \]
  \[3\]
Here, the quotient is 7 and the remainder is 3…………………… (3)
Now since the quotient is not equal to zero therefore, we again need to divide the resulting quotient by 9.
Hence on dividing we get:-
   \[\underline {{\text{ }}} \]
\[9)7(0\]
 \[\underline { - 0} \]
 \[{\text{7}}\]
Now here the quotient is 0 and the remainder is 7…………………… (4)
Now since we have the quotient as zero therefore, we don’t have to divide it further.
Now we will write all the remainders obtained in each step together in order to get the desired answer.
Hence writing all the remainders together we get:-
\[ = 7338\]

Hence, the number 5381 in powers of nine is 7338.

Note:
Students might make mistakes in writing the remainders together. They should note that the remainders are to be written in reverse order i.e. the last remainder obtained is to be written first and the first remainder obtained is to be written at the last.
Also, we have to terminate the division only when the quotient becomes zero.