How do you use scientific notation to solve a problem?

Question

Like for example 9.2*10 to the 12th-3.5*10 to the ninth?

Answer 1

Hi, Kaimi - I found this example from "Dr. Math" of the Math Forum.

Date: 11/03/97 at 09:38:22
From: Doctor Pipe
Subject: Re: Scientific Notation

Hello,

First, when I write exponents at the keyboard, I write 10^6 (for
example). It types in quicker and takes up less space than writing
"10 to the sixth power."

Now, the thing to remember when working with scientific notation to do
multiplication is the law of exponents that says:

a^m x a^n = a^(m+n)

For example, 10^6 x 10^6

= 10^(6+6)
= 10^12

Notice that the base has to be the same in both numbers! You can not
apply the above law of exponents to 10^6 x 5^6 because the bases are
different - the first number has a base of 10 and the second has a
base of 5.

Getting back to your problem, you already know that
4,567,839 = 4.567839 x 10^6 and that 5,493,711 = 5.493711 x 10^6 .

This makes the problem (4.567839 x 10^6) x (5.493711 x 10^6) .

Applying the Associative Property of Multiplication

a x (b x c) = (a x b) x c

and the Commutative Property of Multiplication

a x b = b x a

we get:

(4.567839 x 5.493711) x (10^6 x 10^6)

By multiplying the two left-most factors and applying the above law of
exponents to the right-most factors we get:

25.094387 x 10^12

So, in a nutshell, we converted our large numbers to scientific
notation, added together the exponents where we had common bases, and
then multiplied the non-exponentiated numbers.

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

This link ought to be helpful. Good luck!

Answer 2

It make larger numbers into a more easily hadled format... Also make multiplication and division of large numbers very easy. For subtraction , change both to a common exponent and subtract as normal. 9.2 x 10^12 becomes 9200 x 10^9. Then subtract coefficients as normal

Answer 3

enable ^ = an exponent 4 * 10^3 * 7 * 10^2 4 * 7 * 10^3 * 10^2 28 * 10^5 <============ basically upload the exponents for powers of 10 ...................................... then readjust your decimal factor. 2.8 * 10^6

Answer 4

9.2*10^12=9.2^10^9^10^3
so 9.2^10^12+3.5*10^9
=9.2^10(*10^3+3.5*10^9
=10^9[9.2*10^3+3.5]
10^9[9200+3.5]
=10^9*9203.5
=9.2035*10^12