The Correct Answer and Explanation is:
Correct Answer:
4.6 × 10^5
Explanation:
Scientific notation provides a concise way to write very large or very small numbers. The standard format is a × 10^n, where ‘a’ is a number greater than or equal to 1 but less than 10 (this part is called the coefficient), and ‘n’ is an integer that represents the power of 10 (this part is called the exponent).
To write the number 460,000 in scientific notation, we must follow a two-step process to find the values for ‘a’ and ‘n’.
First, we identify the coefficient ‘a’. We start with the original number, 460,000. For a whole number, the decimal point is assumed to be at the end: 460,000. . Our goal is to move this decimal point to a new position so that there is only one non-zero digit to its left. We achieve this by moving the decimal point to the left, past the zeros and the 6, until it is right after the first digit, 4.
Let’s count the number of places we move the decimal:
Original position: 460000.
Move 1 place: 46000.0
Move 2 places: 4600.00
Move 3 places: 460.000
Move 4 places: 46.0000
Move 5 places: 4.60000
After moving the decimal point 5 places to the left, we get the number 4.6. This value satisfies the condition for our coefficient ‘a’, as it is between 1 and 10.
Second, we determine the exponent ‘n’. The value of the exponent is equal to the number of places we moved the decimal point. In this case, we moved it 5 places. We must also determine the sign of the exponent. Since the original number, 460,000, is a large number (greater than 1), the exponent will be positive. If we were converting a small decimal, the exponent would be negative. Therefore, our exponent ‘n’ is 5.
Finally, we combine the coefficient and the exponent into the scientific notation format, a × 10^n. By substituting the values we found, we get the final answer: 4.6 × 10^5.
