Pre-Algebra Louis D Anjou

Pre-Algebra Louis D’Anjou

Exponents and Scientific Notation

Note: an where (a) = base, (n) = exponent

Rule 1: a0 = 1

Example: 20 = 1; x0 = 1; 2340 =1; 100 = 1

Rule 2: a-n = 1/an

Example: x-5 = 1/x5 ; 5-3 = 1/53 =1/125,

Rule 3: am.an = am+n

Example: 23. 22 = 25 = 32; x3. x5 = x8

Rule 4: am/an = am-n

Example: 25/22 = 25-2 = 23; 104/102 =102 =100

Rule 5: (am)n = am.n

Example: (23)2 = 26 = 64; (32)2 = 34 = 81

(10)3 =103 = 1000; (32)2 =81

Exponents and Scientific Notation (cont’d)

· Scientists have developed a shorter method to express very large or small numbers.

· Scientific Notation is based on powers of the base number 10.

· The standard number 123,000,000,000 in scientific notation is written as :

1.23 x 1011

· The standard number 0.0000000000123 in scientific notation is written as :

1.23 x 10-11

1.23E-11 or as 1.23 X 10^-11

· The first number 1.23 is called the coefficient.

· It must be greater than 1 and less than 10.

· The second number is called the base.

Example Set 2:

a. 960,000 = 9.6 x 105

b. 0.00021 = 2.1 x 10-4

c. 1520 = 1.52 x 103

d. 0.000000113 = 1.13 x 10-7

e. 912,456,700 = 9.12 e+08

f. 0.0000043 = 4.3 e-06

g. 0.0073 = ?

h. 437,560,000 = ?

C3) (y-3)-4 = d3) (106)-4 =

E1) x5. X9 = f1) y5. y-3 =

E2) m-6. m-4 = f2) 105. 10-2 =

E3) 36. 3-3 = f3) 2-7. 24 =

Example Set2:

G1) 108/105 = h1) 25/25 =

G2) p-7/p5 = h2) k-8/k-6 =

G3) m9/m9 = h3) 665/664 =

I1) 7870 = j1) 4p0 =

I2) k0 = j2) 4x0 =

K1) (y6)3 = l1) (p8)-1 =

K2) (102)-2 = l2) (-103)-4 =

K3) (-103)-1 = l3) (-103)-1 =

M1) k5.k-2 = n1) 26.22.2-4 =

M2) 36.3.3-5 = n2) 103.10.10-7 =

M3) x4.x-2 = n3) y6.y-2.y-4 =