Evaluate the expression. Write the answer in standard form.

Question

(-4 x 10^-6) (2 x 10^4) =?

Answer 1

The first step in multiplying numbers in scientific notation is to group the constants and the powers of 10

(-4 X 2)(10^-6 X 10⁴)

Now that they are regrouped, we can multiply the constants and add the powers of ten.  This produces an answer is scientific notation.

-8 X 10^-2

To change an expression in scientific notation into standard notation, move the decimal point the number of places equal to the exponent on the 10.  If it is negative, the decimal point moves to the left.  For this problem, we are moving the decimal point 2 places to the left.

-.08

 

Answer 2

The easiest way to answer this type of question is to multiply all four terms together.  You can do this because multiplication is commutative; it doesn't matter how the terms are organized as long as all are included in the final product.

(-4) (10^-6) (2) (10^4)

First, multiply -4 and 2.  The product is -8.

Then, multiply 10^-6 and 10^4.  When multiplying two or more numbers with the same base and different exponents, the product is the base raised to the sum of the exponents.  For example, if you wanted to multiply 2^2 and 2^3, the final product is 2^5 or 32.  Note that 2^2 = 4, 2^3 = 8, and 4 x 8 = 32.

So, 10^-6 x 10^4 = 10 ^ (-6 + 4) = 10^-2.

The final answer is -8 x 10^-2.

Because 10^-2 = 1 / 10^2 = 0.01, the final answer can also be expressed as -0.08.