Problem 68 - College Algebra Essentials

Question

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

Step-by-Step Solution

Answer

The decimal notation of \(7 \times 10^{-5}\) is 0.00007.

Step 1: Understanding the Scientific Notation

In the number \(7 \times 10^{-5}\), we notice that there is a positive integer (7) and \(10^{-5}\), which has a negative exponent. This means we are dealing with a decimal number that is less than 1.

Step 2: Applying the Negative Exponent Rule

A negative exponent tells us to reciprocate the base to make the exponent positive. However when 10 is raised to any negative power, it simply means we move the decimal point of the number coupled with it to the left by as many places as the value of the negative exponent.

Step 3: Conversion to Decimal Notation

In the given number, since the exponent is -5, we move the decimal point in the number 7 to the left by 5 places. Since there are more places to move than there are digits in the number 7, we fill in the extra places with zeros. Thus, the decimal notation of \(7 \times 10^{-5}\) is 0.00007.