Units of Seven
Find the units digit of 7189. Determine a general rule for
finding the units digit of 7n, where n is any whole number.
This problem asks you to find
the units digit of 7189 and to see if there is a formula to come
up with the units digit for any power.
Solve/Investigate the Problem
Initially, my plans were to use
Microsoft Excel and create a spreadsheet to solve it.
of the Problem
I started by making two columns
in a spreadsheet. I labeled the
first column exponents and it consisted on numbers 0-189. In the second column, I created a
formula that has raised 7 to the power listed in the first column. Once I did this, I could see a
pattern forming. The pattern,
starting with 70 , was 1 7 9 3 1 7 9
3. Based on this, I created a
third column that continued the pattern to the end of the list. Based on this information, the units digit of 7189 would be 7.
After further review, we
determined that you can tell what the units digit
of any number will be by dividing the exponent by 4 if the base is 7. If you divide the exponent by 4 and
your remainder is one, the unit digit is 7. If you divide the exponent by 4 and
your remainder is two or three, the unit digit is 9 or three accordingly. If the exponent divides evenly by
four, the remainder will always be one.
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