How can the number 0.0036 be expressed in scientific notation?

• A. 3.6 x 10^3
• B. 3.6 x 10^-3
• C. 36 x 10^-4
• D. 36 x 10^2

Answer: (B)

To express the number 0.0036 in scientific notation, we need to rewrite it in the form of ( a \times 10^n ), where ( 1 \leq a < 10 ) and ( n ) is an integer.

Starting with 0.0036, we first move the decimal point to the right until we have a number between 1 and 10. In this case, we move the decimal point three places to the right to obtain 3.6. This gives us the coefficient ( a = 3.6 ).

Next, we need to account for the movement of the decimal in terms of powers of 10. Since we moved the decimal 3 places to the right, we express this movement as ( 10^{-3} ). Thus, we combine ( a ) with this power of 10 to write the number as ( 3.6 \times 10^{-3} ).

This reasoning leads us to conclude that the correct expression for 0.0036 in scientific notation is ( 3.6 \times 10^{-3} ), confirming that this option is indeed the correct choice.