Monday, August 11, 2014

214: Last Digit

What is the last digit (units digit) in the expansion of 39999?

How can we find this digit with tech?
Without tech?

Which way is more "clever"?
Which way gives you more satisfaction?

1 comment:

  1. i really like this and am going to use it in my unit on exponents.

    as i was working on james tanton's problem today:
    i started thinking about perfect squares and the kinds of interesting open questions you could ask a student.

    like for example, is there an integer that when you square it the last digit will be 7? why/why not?

    or, x is an integer multiple of 10...what's the last digit of (x-1)^2?
    or, x is an integer multiple of far apart are (x-1)^2 and (x+1)^2?

    or an integer is squared and the result is a 5 digit number with the last digit 4. what could the integer be? what's the lowest value? what's the highest value?

    so much fun stuff!!!