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)
How many times less is 10^2 than 10^6? Express your answer as an integer power of 10.(1 point)
$10^2$ is $10^4$ times less than $10^6$.
Roughly, it takes light less than 0.000000003 of a second to travel a one-meter distance. Express this number in the form of a × 10^n where 1 < a < 10 and is a one-digit number.(1 point)
In scientific notation, we can express the number as $3 \times 10^{-9}$.
To express the federal debt of Country C at the end of fiscal year 2004 in scientific notation, we need to rewrite the number as a single digit multiplied by a power of 10.
The federal debt is $278,560,125,000.
To get a single digit, we divide the number by 10 repeatedly until we have a number between 1 and 10. In this case, we can divide by 10 two times: 278,560,125,000 ÷ 10 ÷ 10 = 278,560,125.
The power of 10 is then determined by the number of times we divided by 10. Since we divided twice, the power of 10 is 10^2 = 100.
Therefore, the closest estimation of the federal debt is approximately 2.786 x 10^11.
To determine the closest estimation of the federal debt of Country C at the end of fiscal year 2004, you can use the concept of scientific notation.
In scientific notation, a number is written as the product of a single digit between 1 and 9 (inclusive) and an integer power of 10. The integer power of 10 represents the number of times the decimal point is moved to the right or left to convert the number to its standard form.
To express the federal debt of Country C in scientific notation, follow these steps:
1. Count the number of digits in the given amount, excluding any decimal point or commas. In this case, there are 12 digits (1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 0, 0).
2. Determine the location of the decimal point by counting from the rightmost digit. In this case, the decimal point is located after the last digit (immediately after the third zero).
3. Express the number in scientific notation by moving the decimal point to the left of the first non-zero digit (between 2 and 7 in this case) and multiplying it by an appropriate power of 10. In this case, the decimal point needs to be moved 11 places to the left.
Therefore, the closest estimation of the federal debt of Country C at the end of fiscal year 2004 in scientific notation is approximately 2.7856 × 10^11.