Problem 80 - College Algebra Essentials

Question

Write each number in scientific notation. $$579,000,000,000,000,000$$

Step-by-Step Solution

Answer

The scientific notation for 5790000000000000000 is \(5.79 \times 10^{18}\).

Step 1: Identify the Significand

The significand \(a\) is found by placing a decimal point after the first non-zero digit in the number. In this case, the number is 5790000000000000000. Moving from left to right, the first non-zero digit is 5. So, the decimal is placed after this number to get 5.79.

Step 2: Identify the Exponent

The exponent \(n\) is found by counting the number of digits to the right of the decimal in the original number. Here, the original number is 5790000000000000000 and we have moved the decimal 18 places to the right. Thus, the exponent \(n\) is 18.

Step 3: Write in Scientific Notation

The number in scientific notation is obtained by combining the significand and the exponent from steps 1 and 2. The final answer is \(5.79 \times 10^{18}\)