Scientific and Standard notations

Question

Write these numbers in standard form. 

 

4.62 • 10^-7

(2 • 10^4)^-2

 

Write these numbers in scientific notation. 

 

(2.6 • 10^-7)(5.3 • 10^6)

(2 • 10^4)^-2

Answer 1

4.62 • 10^-7 = 0.000 0004 62  because exponent of ten, -7, tells you to shift the decimal point 7 places to the LEFT.*
(2 • 10^4)^-2 = 20000 because the 4th power of ten means shift the decimal lpoint 4 places to the RIGHT.

(2.6 • 10^-7)(5.3 • 10^6) = 13.78 × 10^-1 = 1.378  Note that we add the two exponents of ten to get -1 exponent.
(2 • 10^4)^-2 = reciprocal of (2 • 10^4)^2 = reciprocal of 4• 10^8 = 0.25 × 10^-8 = 0.0000 0000 25 *

 

*Note: spacing employed to enhance readability