Simplify and write in scientific notation.

Question

a) (3.24 × 10³)(6.25 × 10^-6)

 

b)1.56 × 10^-2/3.25 × 10^-7

Answer 1

a) (3.24 × 10³)(6.25 × 10^-6)

 

    = (3.24*6.25)*(10^3+(-6)) =

 

    = 20.25*10^-3

 

    = 2.025*10^-2

b) 1.56 × 10^-2/3.25 × 10^-7

 

    = (1.56/3.25)*(10^-2-(-7))

 

    = 0.48*10⁵

 

    = 4.8*10⁴

Answer 2

When multiplying:

 

Multiply the constants.  Add the exponents of common bases.

 

 

When dividing.

 

Divide the constants.  Subtract the exponents of common bases.

 

 

a)

 

(3.24 × 10³)(6.25 × 10^-6) =

 

(3.24 × 6.25) × (10^{3 + (-6)}) =

 

20.25 × 10^-3

 

The constant number must be a number between 1 and 10.  So we move the decimal point 1 place to the left to get 2.025 and add 1 to the exponent.

 

2.025 × 10^-2

 

 

Try the next one on your own.  It will a division problem.  Apply the concept that I mentioned earlier.