Standard Index Form – Numbers Less than 1

For a number less than 1, the power is negative when expressed in standard form.

Worked Example 7.2.1:

Express these numbers in standard form 

a. 0.000587
b. 0.000 000 218
c. 0.000 067
d. 0.000 000 298
e. 0.000 002

Solution

a. 0.000 587

Move the decimal point in between the first two significant digits  

(5 and 8)

= 5.87 × 10^-4

b. 0.000 000 218

= 2.18 × 10^-7

c. 0.000 067

= 6.7 × 10^-5

d. 0.000 000 298

= 2.98 × 10^-7

e. 0.000 002

=  2 × 10^-6

Example 2

Express the following as decimal fractions

a. 4.5 × 10^-2

b. 2 × 10^-5

c. 7.85 × 10^-4

Solution

a. 4.5 × 10^-2

=  0.045

b. 2 × 10^-5

=    0.00002

c. 7.85 × 10^-4

=    0.000785