Problem 72 - College Algebra Essentials

Question

Write each number in decimal notation without the use of exponents. $$6.8 \times 10^{-1}$$

Step-by-Step Solution

Answer

The decimal notation of \(6.8 \times 10^{-1}\) without exponents would be 0.68.

Step 1: Understand the function of the negative exponent

An exponent of -1 indicates that the base, in this case 10, is in the denominator of a fraction. Specifically, \(10^{-1}\) means \(\frac{1}{10}\). Therefore, multiplying a number by \(10^{-1}\) essentially divides that number by 10, which has the effect of moving the decimal point one place to the left.

Step 2: Applying the exponent to the base number

Knowing that \(10^{-1}\)means \(\frac{1}{10}\), we can apply this to the number 6.8. So, \(6.8 \times 10^{-1}\) is the same as dividing 6.8 by 10, which gives 0.68.

Step 3: Write the answer.

So, \(6.8 \times 10^{-1}\) written in decimal notation, without exponents, is 0.68.