Question

1. A student wrote the numeral 572B6 to represent a quantity in base six. a) Sketch the way they packaged the quantity.

b) Identify the packaging rule that was not followed.
c) Repackage correctly.

d) At a glance, how could you have known that 572 is not a valid numeral in base six?

2. Jan Carlos was confused when counting that 1000 is the number after 999. How would you help Jan Carlos understand?

Answer 1

solution:

1.)

a)

They have quantity   , since they wanted to represent this quantity in base six then they had to divide by 6 and found a reminder, in this case 2, that is,

.

Since they have 572B6, they had to divide by 6 and found a reminder, in this case 7, that is,

And finally, they had to divide by 6 and found a reminder, in this case 5, that is,

,

where is an integer number such that .

b)

But in the second division

they made a mistake because , thus the equation should be

c)

If we replace the second equation but we want 5 as a reminder in the third equation we have these equations:

where can be different from (but ) and the numeral is 512B6.

If we replace the second equation and we don't want to keep the last reminder we have as last equation

where is an integer number such that . If then the numeral is otherwise is .

d)

This is because there is 7 . Remind in base 6 there are only 6 digital : 0,1,2,3,4 and 5.

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