Problem 71 - College Algebra Essentials

Question

Write each number in decimal notation without the use of exponents. $$7.9 \times 10^{-1}$$

Step-by-Step Solution

Answer

The decimal notation of \(7.9 \times 10^{-1}\) without using exponents is 0.79.

Step 1: Identify the Elements

Recognize that in the term \(7.9 \times 10^{-1}\), 7.9 is the coefficient and -1 is the exponent.

Step 2: Understand Negative Exponents

A negative exponent implies division by the base, not multiplication. Thus, \(10^{-1}\) is equivalent to \(1/10\).

Step 3: Apply the Exponent’s Effect

To convert a number from scientific notation to decimal notation, you shift the decimal point in the coefficient to the left or right as many places as signified by the exponent. Because we have a -1 exponent, we move the decimal point in 7.9 one place to the left. So, \(7.9 \times 10^{-1}\) becomes 0.79.