Problem 73 - College Algebra Essentials

Question

Write each number in decimal notation without the use of exponents. $$-4.15 \times 10^{-3}$$

Step-by-Step Solution

Answer

-0.00415

Step 1: Understanding scientific notation

Scientific notation is a way to express very large or very small numbers. A number written in scientific notation is written as a product of a number (between 1 and 10) and a power of 10. The number provided is -4.15, and it is multiplied by \(10^{-3}\). This negative exponent means that the decimal point should be moved 3 places to the left.

Step 2: Move the decimal point

The current position of the decimal point is between the digits 4 and 1. To convert this into a pure decimal number we move the decimal point 3 places to the left. Since there aren’t enough numbers on the left, you fill the empty places with zeros.

Step 3: Write the final answer

After moving 3 places to the left, the decimal is before the first zero. Thus, the final answer is -0.00415.