Problem 85 - College Algebra Essentials

Question

Write each number in scientific notation. $$-0.00000000504$$

Step-by-Step Solution

Answer

The scientific notation of \(-0.00000000504\) is \(-5.04 \times 10^{-9}\)

Step 1: Identify the Decimal Point

Find where the decimal point is in the number \(-0.00000000504\). In scientific notation, the decimal point should be after the first non-zero number.

Step 2: Determine the Exponent

Count how many places the decimal point must move in order to be after the first non-zero number. In this case, the decimal point moves 9 places to the right. Since the original number is less than 1, the exponent in the scientific notation will be \(-9\). The exponent is negative because we are dealing with a number less than 1.

Step 3: Write Down the Result

The decimal point is moved to the right until it is positioned after the first nonzero digit. The number of places moved is then noted as a power of 10 and this forms the scientific notation of the number. The negative sign in this case doesn’t affect the conversion process but it remains part of the number.