Associated Topics || Dr. Math Home || Search Dr. Math

### Scientific Notation

```
Date: 08/19/97 at 03:27:49
From: Anthony Raciti
Subject: Scientific notation

Write these numbers in scientific notation:

(a) 55000
(b) 250 000
(c) x
(d) 0.55
(e) 0.000 25
(f) 0.000 000 000 08
```

```
Date: 08/25/97 at 12:15:48
From: Doctor Rob
Subject: Re: Scientific notation

Writing numbers in scientific notation is to put them in the form
a*10^b, where 1 <= a < 10 and b is an integer.

Moving from left to right through the digits of the number, find the
first one which is nonzero. Copy it and all the following digits.
Put a decimal point after this digit. Truncate trailing zeroes.

Now figure out what power of 10 you have to multiply by this to get
the original number. This is the same as the number of digits the
decimal point has moved, with a + sign if it moved to the left and a
- sign if it moved to the right.

Example:

(a) The first nonzero digit is the leftmost 5. Copy down the digits
55000 .  Put the decimal place after the leftmost 5:  5.5000 .
Truncate the trailing zeroes to get 5.5 .  Since the decimal point has
moved 4 places to the left, the power of 10 is +4, and the answer is
5.5*10^4 .

Note: (c) is a trick. Since you don't have any idea what size x is,
it can't be written in scientific notation.

You can do the rest.

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

```
Date: 08/20/97 at 18:17:06
From: Doctor Barney
Subject: Re: scientific notation

In science, we often deal with very large or very small numbers.
Numbers like 900,000,000 or 0.0000003. When numbers are written in
this form, they can be very difficult to manipulate.  For example,
how would you multiply the two numbers I just gave you?

In scientific notation, we write the number as the product of two
different parts.  The first part is a number between one and ten,
like 5.5 or 2.5. Numbers between one and ten are usually pretty easy
to manipulate. The second part is a power of ten.  That just means 10
or 100 or 1000 or 100,000,000,000 or 0.01 or 0.00001, but instead of
writing all those zeros, we write it as an exponent. For example,

100 = 10^2  (ten squared)
100,000 = 10^5  (ten to the fifth power)
0.001 = 10^-3 (ten to the minus three)

Every rational number can be written as the product of a number
between one and ten, and a power of ten. For example,

900,000,000 = 9x10^8
0.0000003 = 3x10^-7

These numbers are very easy to multiply because 9x3 = 27 and
10^8 x 10^-7 = 10 (remember that when you multiply two numbers with
the same base you can just add the exponents). The final answer is
27x10 = 270.

There is a shortcut you can use if you want to. Move the decimal point
to the right or to the left until you have a number between one and
ten. Count the number of places you had to move the decimal point and
that number is the exponent in your scientific notation, except that
the exponent will be negative if you had to move the decimal point to
the right.

For example, to get from 900,000,000 to 9, I had to move the decimal
point 8 places to the left. To get from 0.0000003 to 3 I had to move
the decimal point 7 places to the right

-Doctor Barney,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
```
Associated Topics:
Elementary Large Numbers
Elementary Square Roots
Middle School Exponents

Search the Dr. Math Library:

 Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words

Submit your own question to Dr. Math
Math Forum Home || Math Library || Quick Reference || Math Forum Search