Problem 68 - College Algebra

Question

Write each number in decimal notation without the use of exponents. $$7 \times 10^{-5}$$

Step-by-Step Solution

Answer

The expression \(7 \times 10^{-5}\) in decimal notation without the use of exponents is 0.00007.

Step 1: Understand Negative Exponent Rule

A negative exponent such as \(-5\) in \(10^{-5}\) represents a reciprocal. Therefore, \(10^{-5}\) is equivalent to \(1 / 10^{5}\).

Step 2: Convert to Decimal Notation

Given the rule from Step 1, \(1 / 10^{5}\) equals to \(0.00001\).

Step 3: Apply the Multiplication

Multiply \(0.00001\) (which is the decimal equivalent of \(10^{-5}\)) by 7 to obtain the result in decimal notation.