**1. In the following decimal, how many 2's are there in all before the hundredth 3?**

** **

** 0.23223222322223...**

** **

**2. What is the units digit in the power of 3 with an exponent corresponding to the current year? For example, **

** what is the units digit in the expansion of 3**^{2009} ?

**3. What is the units digit in the expansion of 7**^{1999} ?

**4. What is the tens digit in the expansion of 7**^{1999} ?

**5. What is the digit in the tens place in the expansion of 3**^{2001} ? (Hint: The tens digit repeats in cycles of 20.)

**6. A number is formed by writing the counting numbers in order:**

**123456789101112131415...**

**What is the one millionth digit in this number?**

**Reference**

**Sobel, M & Maletsky, E. (1999). Teaching Mathematics. Allyn &Bacon, Needham Heights, MA**

## Comments (2)

## Lorenzo McWilliams said

at 6:22 pm on Feb 28, 2010

mr wisdom how am i supposed to find the powers of all of these large numbers, it impossible

## Jameswoods said

at 5:05 pm on Aug 24, 2010

i know right man

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