+0

# Base 5 number

0
509
3

If A, B, and C are the digits of the base-five number ABC, which is equal to the base-10 number 47,what does digit B represent?

Dec 26, 2018

#1
+3

We can convert  47  base 10 into base 5. This probably isn't the best way to do it but this is the easiest for me...

_     _     _

25    5     1

how many 25's fit into 47? just 1.

1     _     _

25    5     1

47 - 25  =  22  so there is 22 left.

how many 5's fit into 22? 4.

1     4     _

25    5     1

22 - 20  =  2  so there is 2 left.

how many 1's fit into 2? 2.

1     4     2

25    5     1

47 base 10  =  142 base 5

B = 4

Dec 26, 2018
#2
+1

Maybe other ways to do this...but....

The largest that A can be is 1

47 - 1*5^2 =

47 - 25 = 22

This implies that B = 4  because    4(5) = 20

And C = 2

4710   =   1425

So

B =  4   Dec 26, 2018
#3
+1

Here's one more method :

47 / 5  =  9   Remainder  2

9 / 5  =   1 Remainder  4

1 / 5 =   0 Remainder  1

Reading the red digits from bottom to top  gives us    1425   Dec 26, 2018