A. Approximating powers of p is actually quite simple. For this page, there will be two types of approximations:
1. This approximation only works for powers up to 6 (just for the even powers. The odd powers can go up as high as you need.)
| p1 | 3 | p2 | 10 |
| p3 | 30 | p4 | 100 |
| p5 | 300 | p6 | 1000 |
| p7 | 3000 |
Note: Use this chart if you have to solve expressions.
2. This approximation works for A LOT of powers of n. Use this chart if asked only for pn:
| p1 | 3 | p2 | 9.4 |
| p3 | 30 | p4 | 94 |
| p5 | 300 | p6 | 940 |
| p7 | 3000 | p8 | 9400 |
| p9 | 30000 | p10 | 94000 |
| p11 | 300000 | p12 | 940000 |
| p13 | 3000000 | p14 | 940000 |
etc...
a. I am sure you can see the pattern, but if you need help remembering:
1. If n is odd: Write 3 + (n-1)/2 zero's.
2. If n is even: Write 94 + (n/2 - 2) zero's.
C. Here are a few examples:
Ex [1] p8 = __________.
a. Since 8 is even the approximate answer is 9400.
b. Note: Most problems will be of this type.
Ex [2] (3p)6 = __________.
a. This time use the first table or p6 = 1000.
b. 36 = 729.
c. 729 x 1000 = 729000.
d. The answer can be between: 665810 and 735895.