Sum of 7’s

In the sum of the expression 7+77+777+7777+\cdots+7,\!777,\!777,\!777,\!777,\!777,\!777, what digit will be in the tens place?
Source: NCTM Mathematics Teacher, February 2008

Solution
We are adding nineteen numbers from the smallest 7 to the largest 7,\!777,\!777,\!777,\!777,\!777,\!777. Note that there are nineteen 7\mathrm{'s} in the ones place and eighteen 7\mathrm{'s} in the tens place. First, we add the nineteen 7\mathrm{'s} in the ones place and get 19\times 7=133. Consider the number 133. The 3 in the ones place of 133 will be the ones place digit of the final sum. The 3 in the tens place of 133 means 30 and if we regroup 30 with the eighteen 70\mathrm{'s}, we get 30+18\times 70=1290. The digit in the tens place of the final sum is 9.

Answer: 9

Advertisements

About mvtrinh

Retired high school math teacher.
This entry was posted in Problem solving and tagged , , , , . Bookmark the permalink.

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google+ photo

You are commenting using your Google+ account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s