Question

EVALUATING EXPRESSIONS Evaluate the expression without using a calculator. Write the result in scientific notation and in decimal form. $$ \left(6 \times 10^{5}\right) \cdot\left(2.5 \times 10^{-1}\right) $$

Short answer

The solution to the expression is \(15 * 10^{4}\) in scientific notation and 150000 in decimal form.

Step-by-step solution

Multiply Coefficients

Multiply the coefficients of the terms, which are 6 and 2.5 in this case. The calculation will be \(6 * 2.5 = 15\).

Combine the Powers of 10

Combine the powers of 10 by adding the exponents, applying the rule \(10^{n+m}\). The powers are 5 and -1, so the calculation will be \(10^{5 + -1} = 10^{4}\).

Put Together the Result in Scientific Notation

Combine the result from step 1 and step 2 to write the answer in scientific notation. The product of the coefficients becomes the new coefficient, and the sum of the exponents becomes the new exponent. Therefore, the solution in scientific notation is \(15 * 10^{4}\).

Convert to Decimal Form

To convert \(15 * 10^{4}\) into decimal form, move the decimal in 15 four places to the right (because of \(10^4\)), resulting in \(150000\).