The Correct Answer and Explanation is:
Correct Answer
The first box should contain 6.67.
The second box (the exponent) should contain 4.
The complete scientific notation is 6.67 x 10⁴.
Explanation
Scientific notation is a standard way to write very large or very small numbers concisely. The format is always a number between 1 and 10, called the coefficient, multiplied by a power of 10. To convert the number 66,700 into this format, we follow a two-step process.
First, we need to determine the coefficient. This is done by adjusting the original number so that it falls between 1 and 10. For 66,700, the decimal point is understood to be at the very end (66,700.). To make this number meet the requirement, we must move the decimal point to the left until there is only one non-zero digit in front of it. Moving the decimal point one place gives us 6,670.0. Moving it again gives 667.00, then 66.700, and finally 6.6700. The number 6.67 is between 1 and 10, so it becomes our coefficient.
Second, we determine the exponent for the power of 10. The exponent is simply the number of places we moved the decimal point in the first step. In this case, we moved the decimal point four places to the left. Because the original number, 66,700, is a large number (greater than 1), the exponent will be positive. Therefore, the exponent is 4.
By combining the coefficient and the power of 10, we get the final answer. The scientific notation for 66,700 is 6.67 × 10⁴. We can verify this by calculating 6.67 multiplied by 10⁴ (which is 10,000), resulting in 66,700, which is our original number.
