Scientific Notation: Adding and Subtracting Exponents

Date: 03/21/2002 at 10:20:24
From: Vicki Moser
Subject: Scientific Notation

How do you add and subtract numbers written in scientific notation 
form?

Date: 03/21/2002 at 10:42:26
From: Doctor Ian
Subject: Re: Scientific Notation

Hi Vicki,

The key is to make sure they have the same exponent. Then you can add 
and subtract them like 'regular' numbers:

    3.14159 * 10^9 + 2.71828 * 10^7

  = 314.159 * 10^7 + 2.71828 * 10^7

  = (314.159 + 2.71828) * 10^7

This is similar to what you have to do to add or subtract fractions:

  2   3   14   15
  - + - = -- + -- = (14 + 15) * (1/35) = 19/35
  5   7   35   35

There's nothing magical about having the same exponent, or the same 
denominator. It just allows you to apply the distributive property:

  ac + bc = (a + b)c

Does this help? 

- Doctor Ian, The Math Forum
  http://mathforum.org/dr.math/   

Date: 03/21/2002 at 11:18:01
From: Vicki Moser
Subject: Scientific Notation

Thank you so much for responding to my question so quickly.