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 Write-up

Title

Units of Seven

Problem Statement
Find the units digit of 7189. Determine a general rule for finding the units digit of 7n, where n is any whole number.

Problem setup

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.

Plans to Solve/Investigate the Problem

Initially, my plans were to use Microsoft Excel and create a spreadsheet to solve it.

Investigation/Exploration 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.

Author & Contact
Benjamin Moore
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