At the end of a fiscal ear 204, the federal debt of County C is $278,560,125,000. What is the closest estimation of this amount? Express your answer in the form of a single digit times an integer power of 10.
2x10^11
2.79x10^11
3x10^-11
3x10^11
The closest estimation of the federal debt of County C is 2.79x10^11.
The closest estimation of the federal debt of County C at the end of fiscal year 204 is 2.79x10^11.
To estimate the given amount, $278,560,125,000, as a single digit times an integer power of 10, follow these steps:
Step 1: Identify the closest power of 10 that makes the number easier to represent.
Since the number is already in the billions, it is convenient to use a power of 10 that ends in 9 zeros.
Step 2: Determine the single digit that represents the value in front of the power of 10.
To do this, divide the given number by the selected power of 10 and round the result to the closest whole number.
Let's use 10^11 as the power of 10. Dividing $278,560,125,000 by $10^11 gives us:
$278,560,125,000 / $10^11 ≈ 2.78560125
Rounding this value to the closest whole number yields 3.
Therefore, the single digit in front of the power of 10 is 3.
Step 3: Write the value in scientific notation.
Now that we have the single digit (3) and the power of 10 (11), we can express the estimated amount in scientific notation.
Thus, the closest estimation of $278,560,125,000 is 3 × 10^11.
Therefore, the correct answer is 3x10^11.