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.
Responses
The closest estimation of the federal debt of Country C at the end of fiscal year 2004 is $280 billion. (Using 2.80 x 10^11 as the scientific notation)
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.
3 × 10−11
2 × 1011
3 × 1011
The closest estimation of the federal debt of Country C at the end of fiscal year 2004 is $280 billion. This can be expressed as 2 × 10^11.
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.
Responses
3 × 10^−11
or
3× 10^11
The closest estimation of the federal debt of Country C at the end of fiscal year 2004 is $278.6 billion. This can be expressed as 2.786 × 10^11.
To express the federal debt of Country C at the end of fiscal year 2004 as a single digit times an integer power of 10, we need to convert the number to scientific notation. Scientific notation is a way of representing large numbers by showing the significant digits multiplied by a power of 10.
The given amount is $278,560,125,000. To convert it to scientific notation, we can move the decimal point 11 places to the left and multiply by 10^11.
$278,560,125,000 = 2.78560125 x 10^11.
Therefore, the closest estimation of the federal debt of Country C at the end of fiscal year 2004 is 2.8 x 10^11.
To estimate the given amount in a form of a single digit times an integer power of 10, we need to round it to the nearest power of 10 that can be represented with a single digit coefficient.
In this case, we have $278,560,125,000. To estimate it, we can convert it to scientific notation, which is expressed as a number between 1 and 10 multiplied by a power of 10.
To convert the number to scientific notation, count the number of digits in the original number after the decimal point. In this case, there are no digits after the decimal point.
Next, we move the decimal point to the left until there is only a single digit to the left of the decimal point. The number of times we move the decimal point determines the power of ten.
Let's start by moving the decimal point to the left once: $27,856,012,500. This can be expressed as 2.78560125 × 10^10.
So, the closest estimation of the federal debt in the form of a single digit times an integer power of 10 is approximately 2.8 × 10^10.