Final answer:
The number 74,905 in scientific notation is written as 7.4905 × 104. Scientific notation simplifies arithmetic operations and is especially helpful for very large or small numbers.
Step-by-step explanation:
When writing the number 74,905 in scientific notation, we first determine the coefficient by placing a decimal after the first non-zero digit, creating 7.4905. Then, we count how many places the decimal needs to move to return to the original number. In this case, the decimal needs to move 4 places to the right, yielding an exponent of 4. Therefore, 74,905 in scientific notation is 7.4905 × 104.
Scientific notation is very useful for dealing with very large or very small numbers, as it simplifies arithmetic operations such as multiplication and division. If a calculation involves multiplication of powers of ten, simply add the exponents, and if there are coefficients in front of the powers of ten, multiply those coefficients separately. This makes mathematical operations much easier compared to using standard form with many zeros.