Quandaries and Queries
 


My son, who is 9 in grade 5 has been asked to convert base 10 numerals into base 5.

His first question of:

24(10) he has calculated to be 4x5 + 4x1 = 44 (5)

The next question however is the tricky one. We know the answer is supposed to be 100 but we find it difficult to get this in the way he understands it.

25 (10) = _________________ 100 (5)

Can you help us figure out how we reach the answer.

I've read the other examples you have on the web site but still find it difficult to understand.

Thanks,

Susy



Hi Susy,

Imagine that you have 25 items and collect them into groups of 5. You get

5 groups of 5 with 0 remainder Now divide the 5 groups of 5 into groups of 5. You get 1 group of (5 groups of 5) with 0 remainder Now divide these into groups of 5. You get 0 groups of (5 groups of (5 groups of 5)) with 1 remainder. Thus you have 1 group of size twenty-five (5 5), 0 groups of size five (5) and 0 groups of size one. That is 1 (5 5) + 0 (5) + 0 = 100(base5)

Another way to say this is

25 divided by 5 is 5 with a remainder of 0
5 divided by 5 is 1 with a remainder of 0
1 divided by 5 is 0 with a remainder of 1.
When you reach a result of 0, you read the remainders from the bottom to the top to get the number in base 5: 100.

For example to write 32 in base 5

32 divided by 5 is 6 with a remainder of 2
6 divided by 5 is 1 with a remainder of 1
1 divided by 5 is 0 with a remainder of 1.
so 32 = 112(base5)

By the way, the sequence 1 (5), 10 (5), 100 (5), 1000 (5), 10000 (5), ... is just the sequence of powers of the base; in base 10 this is 1, 5, 25, 125, 625, ...

Claude and Penny


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