Problem 73 - College Algebra

Question

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

Step-by-Step Solution

Answer

The number \(-4.15 \times 10^{-3}\) can be written in decimal notation as -0.00415.

Step 1: Identify the Given Number

Identify the given number in scientific notation which is \(-4.15 \times 10^{-3}\). Note that the number has a negative exponent.

Step 2: Apply the Rule for Negative Exponents

The rule for a negative exponent is to move the decimal point in the number to the left by the number of places indicated by the absolute value of the exponent. Here, there's an exponent of -3, that means the decimal point in -4.15 should be moved three places to the left.

Step 3: Moving the Decimal Place

Begin from the given number -4.15. The decimal will be moved three places to the left. Therefore, the first move will make it -0.415. The second move gives -0.0415. The third and final move gives -0.00415.

Step 4: Writing the Final Answer

After moving the decimal, we get -0.00415. This is the number -4.15 \times 10^{-3} written in decimal notation without the use of exponents.