Table of Contents | Home

Lesson 21  Section 2

Back to Section 1

Exponent 0

Scientific notation


Exponent 0

Any number (except 0) with exponent 0 is defined as 1.

a0 = 1

Problem 8.   Evaluate the following..

To see the answer, pass your mouse over the colored area.
To cover the answer again, click "Refresh" ("Reload").
Do the problem yourself first!

   a)   50  =  1   b)   (−5)0  =  1   c)   −50  =  −1   d)   (½)0  =  1
   e)   3· 100  =  3· 1 = 3   f)   (3· 10)0  =  1   g)   −3· 100  =  −3· 1 = −3

h)  5 + 50(5 + 50) =  5 + 1(5 + 1) = 5 + 6 = 11

Why do we define a0 as 1?

For one thing, we have this rule:

  = amm = a0.
But
  = 1.

Therefore, we must define a0 as 1.

As for 00, that could be any number! For,

= Any number. Lesson 6

But

= 00.

Therefore we must conclude that 00 could be any number.

Problem 9.   Use the rules of exponents to evaluate the following.

 a)   = 107 − 2 + 3 − 8 = 100 = 1
 b)   = 22 − 8 + 4 + 3 − 6 + 5 = 20 = 1

Scientific notation

"Scientific notation" has one non-zero digit to the left of the decimal point.

2.345

That number is written in scientific notation.  There is one digit to the left of the decimal point -- 2 -- and it is not 0.

In general, a number written in scientific notation will be multiplied by 10 raised to an exponent.

Example 1.   6.45 × 103.  This is the scientific notation for what number?

Answer.   Since the exponent is positive, we will be multiplying 6.45.  To multiply a decimal by a power of 10, move the decimal point right the number of places indicated by the exponent:

6.45 × 103 = 6,450

Move the point three places right.  To do that, we must add on a 0.(Skill in Arithmetic, Lesson 3.)

Example 2.   6.45 × 10−3.  This is the scientific notation for what number?

Answer.   Since the exponent is negative, we will be dividing 6.45.  (For,
10−3    1   
1000
.)  To divide a decimal by a power of 10, move the decimal

point left the number of places indicated by the exponent:

6.45 × 10−3 = .00645

Move the point three places left.  To do that, we must add on 0's.

Problem 10.   Each of these is written in scientific notation.  Multiply out.

  a)   2.401 × 103  =  2,401   b)   1.006 × 10²  =  100.6
 
  c)   7.01 × 105  =  701,000   d)   4.986 × 10  =  49.86
 
  e)   3.85 × 10−4  =  .000385   f)   1.8 × 10−1  =  .18
 
  g)   6.0 × 10−3  =  .006   h)   4.3 × 10−8  =  .000000043

Example 3.   Write in scientific notation.  

a)   562.4 = 5.624 × 102

To change  562.4  into  5.625, we moved the decimal point two places left.  To compensate, we must multiply by 10 with exponent +2.

b)   .00395 = 3.95 × 10−3

To change  .00395  into  3.95, we moved the decimal point three places right.  To compensate, we must multiply by 10 with exponent −3.

Problem 11.   Write in scientific notation.

   a)   1234 = 1.234 × 103   b)   12.34 = 1.234 × 10
 
  c)   219,000,000 = 2.19 × 108   d)   0.000081 = 8.1 × 10−5
 
  e)   0.00395 = 3.95 × 10−3   f)   0.000000002 = 2.0 × 10−9

Next Lesson:  Multiplying and dividing algebraic fractions


Table of Contents | Home


Please make a donation to keep TheMathPage online.
Even $1 will help.


Copyright © 2001-2007 Lawrence Spector

Questions or comments?

E-mail:  themathpage@nyc.rr.com