Question

EVALUATING EXPRESSIONS Evaluate the expression without using a calculator. Write the result in scientific notation and in decimal form. $$ \frac{6.6 \times 10^{-1}}{1.1 \times 10^{-1}} $$

Short answer

The answer is \(6.0 \times 10^0\) in scientific notation and 6 in decimal form.

Step-by-step solution

Separate Coefficients and Powers of 10

Break down the expression by separating the coefficients from the powers of 10. The expression becomes \((6.6/1.1) \times (10^{-1}/10^{-1})\).

Simplify Division

Perform the division of the coefficients and the powers of 10. The division of the coefficients is \(6.6/1.1 = 6\), and for the powers of 10, subtract the exponent in the denominator from the exponent in the numerator, hence \(10^{-1}-(-1) = 10^0\).

Write in Scientific Notation

The simplified expression should be written in scientific notation. Remember that any number raised to the power of 0 is 1, hence \(10^0 = 1\). The scientific notation of \((6 \times 1)\) becomes \(6.0 \times 10^0\).

Convert to Decimal Form

The decimal form of \(6.0 \times 10^0\) is simply 6 because any number multiplied by 1 remains the same.