1. The radius of a hydrogen atom is 0.0000000529177 of a millimeter. Express this number as an approximation.(1 point)%0D%0AResponses%0D%0A%0D%0A0.0000000053%0D%0A0.0000000053%0D%0A%0D%0A0.00000006%0D%0A0.00000006%0D%0A%0D%0A0.0000005%0D%0A0.0000005%0D%0A%0D%0A0.00000005

Question

2. How many times is 4 × 10^4 larger than 2 × 10^2?(1 point)%0D%0AResponses%0D%0A%0D%0A2%0D%0A2%0D%0A%0D%0A2,000%0D%0A2,000%0D%0A%0D%0A200%0D%0A200%0D%0A%0D%0A20

3. 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)%0D%0AResponses%0D%0A%0D%0A2.79 × 10^11%0D%0A2.79 times 10^11 baseline%0D%0A%0D%0A2 × 10^11%0D%0A2 times 10^11 baseline%0D%0A%0D%0A3 × 10^11%0D%0A3 times 10^11 baseline%0D%0A%0D%0A3 × 10^−11

How many times less is 102 than 106? Express your answer as an integer power of 10.(1 point)%0D%0AResponses%0D%0A%0D%0A10^−4%0D%0%0D%0A%0D%0A10^4%0D%0A10%0D%0A%0D%0A0.0001%0D%0A0.0001%0D%0A%0D%0A10,000

5. 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)

3x10^-9
3x10^9
3x10^-8
3x10^8

Answer 1

Let's go through each question one by one:

1. Express the radius of a hydrogen atom as an approximation.

   • The given radius is 0.0000000529177 mm. This can be approximated to:
     • 0.00000005 (which is \(5.29177 \times 10^{-8}\) and rounds to \(5.3 \times 10^{-8}\)), closest option is:
       • 0.00000005

2. How many times is \(4 \times 10^4\) larger than \(2 \times 10^2\)?

   • To find out how many times \(4 \times 10^4\) is larger than \(2 \times 10^2\): \[ \frac{4 \times 10^4}{2 \times 10^2} = \frac{4}{2} \times \frac{10^4}{10^2} = 2 \times 10^{4-2} = 2 \times 10^2 = 200 \]
     • The answer is:
       • 200

3. What is the closest estimation of $278,560,125,000?

   • This number can be simplified to \(2.78560125 \times 10^{11}\). The closest single digit times an integer power of 10 is:
     • 3 × 10^11

4. How many times less is \(10^2\) than \(10^6\)?

   • To determine how many times less \(10^2\) is: \[ \frac{10^6}{10^2} = 10^{6-2} = 10^4 \]
     • The answer is:
       • 10^4

5. Express \(0.000000003\) of a second in the form \(a \times 10^n\).

   • The number can be written as \(3 \times 10^{-9}\):
     • The answer is:
       • 3 × 10^-9

So the final answers in order are:

1. 0.00000005
2. 200
3. 3 × 10^11
4. 10^4
5. 3 × 10^-9