Exponents on a Scientific Calculator

Date: 08/21/97 at 17:10:08
From: David Brownfield
Subject: Using a scientific calculator

This is my first year in Algebra. I am trying to learn to use my new 
scientific calculator. My problem is that I am not using the EXP key 
correctly. I needed to input 8 to the 2nd and I pushed 8 and then the 
EXP key and then 2 and I kept getting 800. I KNOW 8 to the 2nd is not 
800!  What am I doing wrong?

Date: 08/22/97 at 11:02:45
From: Doctor Guy
Subject: Re: Using a scientific calculator

What you are doing is asking the calculator to evaluate 8 x 10^2, 
which is scientific notation. 

If you haven't heard of scientific notation, I'll give you a few 
examples. 

The speed of light is a very large quantity: approximately 186,000 
miles per second or 300,000 km/sec. In scientific notation, these 
quantities would be 1.86x10^5 mi/sec or 3.0x10^5 km/sec. 

These numbers are not too big for your calculator, but if you start 
trying to convert them to miles per hour or km per hour, then they 
get much bigger, because you have to multiply each one by 60 sec/min 
and then by 60 min/hour, so you get 669,600,000 mi/hr or 
1,080,000,000 km/hr, which in scientific notation would be 
6.696 x 10^8 mph or 1.08 x 10^9 km/hr. And if you want to know how 
far light travels in a year (hence, a light-year), you would have to 
multiply these two quantities by 24 hrs/day and then by 365 days/yr, 
to get the truly astronomical quantities 5,865,696,000,000 miles/yr 
or 9,460,800,000,000 km/yr. 

Now if you've been following along with me on your calculator, I bet 
that you probably didn't see the two last answers the way I typed them 
here, because your calculator probably cannot handle numbers that long 
in that form. You probably saw something like 5.85696 E 12 and 
9.4608 E 12. On your calculator, the "E" might be small capitals or 
in lower-case or might be missing entirely, depending on the 
manufacturer. In order to get the answer to fit on the display, the 
calculator simply converted these numbers to a version of scientific 
notation, replacing the "x 10^" with an "E" or an "e" or perhaps just 
a space. 

Why do they do that replacement? It is very inconvenient for most 
calculators (and even for me, typing this here) to write the exponent 
in the correct location and in the correct size (i.e., a bit smaller, 
and in superscript). Therefore, calculators generally use some sort of 
abbreviation. I hope you follow me.

Now I still haven't answered the question of how you actually DO 8^2. 
Problem is, the exact answer to that depends on the manufacturer of 
your calculator, and you didn't say who that was. But in my experience 
with lots of students who have had questions like yours, many 
inexpensive scientific calculators have a key that says on it (in one 
color or another) something like x^y or y^x (sorry, I cannot write 
that properly, in superscript: in other words, there is a regular-
sized x and a little y up to its right, or vice versa). If one of your 
keys has that legend on it, then that's the one you want. 

To raise 8 to the 2nd power, you would type 8, then hit the x^y or 
y^x key, then hit the 2, then hit "=", which should give you 64. Let 
us know if that doesn't work.

If, instead, you have a "^" key, then you would simply type "8^2=", 
but you probably would have figured that out by yourself if you had 
a key like that. I don't know if your calculator came with a manual; 
if it did, then be sure to read it carefully. It's the only source of 
information about exactly how it works. If the manual is lost, well, 
too bad, and you will either have to keep asking questions or else 
experiment systematically with all the keys you don't understand. (On 
many scientific calculators, if you repeatedly hit the EXP key, 
perhaps followed by = or else preceded by the 2nd or FN key, you can 
convert between regular and scientific notation. Give it a try. 
There usually is also a key combination to, say, find the 3rd root 
of 8, which is 2.)

Good luck, and I hope this helped.

-Doctor Guy,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/