The Correct Answer and Explanation is:
Correct Answer:
The number 66,700 written in scientific notation is 6.67 x 10⁴.
In the image provided, you would enter 6.67 into the first box and 4 into the second box.
Explanation
Scientific notation is a standardized way to write numbers that are very large or very small, making them easier to read and work with. A number is expressed in scientific notation when it is written as the product of a coefficient and a power of 10. The general form is a × 10ᵇ, where ‘a’ is the coefficient (a number greater than or equal to 1 but less than 10) and ‘b’ is the integer exponent.
To convert 66,700 into scientific notation, follow these steps:
- Determine the coefficient (a): Start with the number 66,700. The decimal point is implicitly at the end of the number (66,700.). To find the coefficient ‘a’, you must move this decimal point to a position where there is only one non-zero digit to its left. For 66,700, you would move the decimal point between the first and second digit, the two 6s. This gives you the number 6.67. This value satisfies the rule that 1 ≤ a < 10, so our coefficient is 6.67.
- Determine the exponent (b): The exponent ‘b’ is the number of places you moved the decimal point in the previous step. To get from 66,700. to 6.67, you moved the decimal point four places to the left. Since the original number (66,700) is a large number (greater than 1), the exponent will be positive. If you were converting a small number like 0.00667, you would move the decimal to the right, and the exponent would be negative. In this case, since you moved the decimal four places to the left, the exponent is +4, or simply 4.
- Combine the parts: Now, you can write the number in its final scientific notation form by combining the coefficient and the exponent. This results in 6.67 × 10⁴. You can verify this by calculating 10⁴ (which is 10,000) and multiplying it by 6.67, which correctly equals 66,700.
