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) Responses 3 × 10−11 3 times 10 superscript negative 11 baseline 3 × 1011 3 times 10 superscript 11 baseline 2 × 1011 2 times 10 superscript 11 baseline 2.79 × 1011
How many times less is 102 than 106 ? Express your answer as an integer power of 10.(1 point) Responses 10−4 10 superscript negative 4 baseline 0.0001 0.0001 104 10 superscript 4 baseline 10,000 10,000
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 × 10n where 1 < a < 10 and is a one-digit number.(1 point) Responses 3 × 108 3 times 10 superscript 8 baseline 3 × 109 3 times 10 superscript 9 baseline 3 × 10−9 3 times 10 superscript negative 9 baseline 3 × 10−8
The closest estimation of the federal debt of Country C at the end of fiscal year 2004 is 2.79 × 10^11.
102 is 10^-4 times less than 106. So, the answer is 10^-4.
Roughly, it takes light 3 × 10^-9 of a second to travel a one-meter distance.
To find the closest estimation of the federal debt at the end of fiscal year 2004, we need to express the given number in the form of a single digit times an integer power of 10.
The given amount is $278,560,125,000. To express this in scientific notation, we move the decimal point to the left until we have a single digit in front of it. In this case, we can move the decimal point 11 places to the left.
So the closest estimation of this amount would be 2.79 × 10^11.
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To find how many times 102 is less than 106, we can subtract 102 from 106.
106 - 102 = 4
So 102 is 4 times smaller than 106.
Expressed as an integer power of 10, it would be 10^4.
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To express the time it takes light to travel a one-meter distance in the given form, we can express the given number (less than 0.000000003) in scientific notation.
The number can be expressed as 3 × 10^-9.
So the closest estimation would be 3 × 10^-9.
NOTE: There was a typo in the options provided. It should be 3 × 10^-9, not 3 × 10^-8.
To estimate the closest amount to $278,560,125,000, we can round the number to the nearest power of 10. In this case, the number is already in the form of a single digit times an integer power of 10. Therefore, the closest estimation is 2.79 × 10^11.
To determine how many times less 102 is than 106, we need to find the difference between the two numbers and express it as an integer power of 10. The difference between 102 and 106 is 4, and since 102 is a smaller number, we express it as a negative exponent. Therefore, the answer is 10^-4.
When expressing the time it takes for light to travel a one-meter distance, we need to convert the given value into scientific notation with a single digit as the coefficient and an integer power of 10. The given value is less than 1 second, so we express it as a decimal between 1 and 10. In this case, 0.000000003 can be simplified as 3 × 10^-9. Therefore, the answer is 3 × 10^-9.
So, for the given questions, the correct responses are:
1. 2.79 × 10^11
2. 10^-4
3. 3 × 10^-9