At the end of fiscal year 2004, the federal debt of Country 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 (1 point)
0 2 × 1011
0 3 × 10 11
О 3 x 1011
O 2.79 × 1011
The closest estimation of the federal debt at the end of fiscal year 2004 would be $280 billion, which is equal to $2.8 × 10^11 or Option D: 2.79 × 10^11.
To express the given amount, $278,560,125,000, in the form of a single digit times an integer power of 10, we need to move the decimal point to the left until there is one digit to the left of the decimal point.
When we move the decimal point five places to the left, the new value becomes $2,785,601,250,000.
Therefore, the closest estimation of the amount $278,560,125,000 is 3 × 10^11 or 3 x 10^11.
To estimate the given amount, $278,560,125,000, we can determine the closest value in scientific notation.
When expressing a number in scientific notation, we separate it into two parts: a number between 1 and 10 (known as the coefficient) and a power of 10 (known as the exponent).
To find the coefficient, we can divide the given amount by 10 raised to the power of its digits. In this case, the number is in the billions place, so the power of 10 is 11. Therefore, we divide the amount by 10^11:
$278,560,125,000 ÷ (10^11) = 2.78560125
Now, we need to round this coefficient to a single digit. Since the digit after the first decimal place is less than 5, we round down. Thus, the rounded coefficient would be 2.
Now, we express the estimation in scientific notation. The coefficient is 2, and the exponent is 11, as determined earlier. Therefore, the estimated amount is:
2 × 10^11
So, the closest estimation of the federal debt is 2 × 10^11.