Question

Express the decimal number 100 in all radices from 2 to 9

Answer 1

A decimal number can be converted into diffrent radices by continuos division and recording the remainders.


Part 1

To convert the decimal number 100 to radix 2, we have:


`(100)/(2) =50 \ remainder \ 0 \\ \\ (50)/(2) =25 \ remainder \ 0 \\ \\ (25)/(2) =12 \ remainder \ 1 \\ \\ (12)/(2) =6 \ remainder \ 0 \\ \\ (6)/(2) =3 \ remainder \ 0 \\ \\ (3)/(2) =1 \ remainder \ 1 \\ \\ (1)/(2) =0 \ remainder \ 1`

Starting from the bottom we collate the remainders.

Therefore, the value of decimal number 100 in radix 2 is 1100100



Part 2:

To convert the decimal number 100 to radix 3, we have:


`(100)/(3) =33 \ remainder \ 1 \\ \\ (33)/(3) =11 \ remainder \ 0 \\ \\ (11)/(3) =3 \ remainder \ 2 \\ \\ (3)/(3) =1 \ remainder \ 0 \\ \\ (1)/(3) =0 \ remainder \ 1`

Starting from the bottom we collate the remainders.

Therefore, the value of decimal number 100 in radix 3 is 10201



Part 3:

To convert the decimal number 100 to radix 4, we have:


`(100)/(4) =25 \ remainder \ 0 \\ \\ (25)/(4) =6 \ remainder \ 1 \\ \\ (6)/(4) =1 \ remainder \ 2 \\ \\ (1)/(4) =0 \ remainder \ 1`

Starting from the bottom we collate the remainders.

Therefore, the value of decimal number 100 in radix 4 is 1210



Part 4:

To convert the decimal number 100 to radix 5, we have:


`(100)/(5) =20 \ remainder \ 0 \\ \\ (20)/(5) =4 \ remainder \ 0 \\ \\ (4)/(5) =0 \ remainder \ 4`

Starting from the bottom we collate the remainders.

Therefore, the value of decimal number 100 in radix 5 is 400



Part 5:

To convert the decimal number 100 to radix 6, we have:


`(100)/(6) =16 \ remainder \ 4 \\ \\ (16)/(6) =2 \ remainder \ 4 \\ \\ (2)/(6) =0 \ remainder \ 2`

Starting from the bottom we collate the remainders.

Therefore, the value of decimal number 100 in radix 5 is 244



Part 6:

To convert the decimal number 100 to radix 7, we have:


`(100)/(7) =14 \ remainder \ 2 \\ \\ (14)/(7) =2 \ remainder \ 0 \\ \\ (2)/(7) =0 \ remainder \ 2`

Starting from the bottom we collate the remainders.

Therefore, the value of decimal number 100 in radix 5 is 202



Part 7:

To convert the decimal number 100 to radix 8, we have:


`(100)/(8) =12 \ remainder \ 4 \\ \\ (12)/(8) =1 \ remainder \ 4 \\ \\ (1)/(8) =0 \ remainder \ 1`

Starting from the bottom we collate the remainders.

Therefore, the value of decimal number 100 in radix 5 is 144



Part 8:

To convert the decimal number 100 to radix 9, we have:


`(100)/(9) =11 \ remainder \ 1 \\ \\ (11)/(9) =1 \ remainder \ 2 \\ \\ (1)/(9) =0 \ remainder \ 1`

Starting from the bottom we collate the remainders.

Therefore, the value of decimal number 100 in radix 5 is 121