Answered

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(a) Write the next whole number after 222three in the base-three system.

Sagot :

sqdancefan

Answer:

  1000

Step-by-step explanation:

You want the next number after 222 in base 3.

Counting sequence

In any useful number base, the counting at any given integer position is ...

  0, 1, 2, 3, ..., (base -1), 0 and add 1 to the next number position

For base 3, this is ...

  0, 1, 2, 10

When the digit in the next higher position is also (base -1), then it gets incremented to 0 and the carry is propagated to the left.

In base 10, the equivalent is ...

  999 +1 = 99(9+1) = 99(10) = 9(9+1)0 = 9(10)0 = (9+1)00 = 1000

In base 3, your incremented value is ...

  222 +1 = 22(2+1) = 22(10) = 2(2+1)0 = 2(10)0 = (2+1)00 = 1000

The next whole base 3 number after 222 is 1000.

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