Question

The radius of a hydrogen atom is 0.0000000529177 of a millimeter. Express this number as an approximation.(1 point)
Responses

0.00000005
0.00000005

0.00000006
0.00000006

0.0000005
0.0000005

0.0000000053

How many times is 4 × 10(4)
larger than 2 × 10(2)
?(1 point)
Responses

2
2

2,000
2,000

20
20

200


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

2 × 1011
2 times 10 superscript 11 baseline

3 × 10−11
3 times 10 superscript negative 11 baseline

3 × 1011
3 times 10 superscript 11 baseline

2.79 × 1011
2.79 times 10 superscript 11 baseline


How many times less is 10(2)
than 10(6)
? Express your answer as an integer power of 10.(1 point)
Responses

10,000
10,000

10(−4)
10 superscript negative 4 baseline

10(4)
10 superscript 4 baseline

0.0001

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)
Responses

3 × 10(−8)
3 times 10 superscript negative 8 baseline

3 × 10(−9)
3 times 10 superscript negative 9 baseline

3 × 10(8)
3 times 10 superscript 8 baseline

3 × 10(9)

Answer 1

Let's address each question one by one.

1. **Expressing the radius of a hydrogen atom:**
The value given is 0.0000000529177 mm. When approximating to a significant figure, we can round it to 0.00000005, which is the most suitable given the options.
**Response:** 0.00000005

2. **Finding how many times larger 4 × 10^4 is than 2 × 10^2:**
We can express this as:
\[
\frac{4 \times 10^4}{2 \times 10^2} = \frac{4}{2} \times \frac{10^4}{10^2} = 2 \times 10^{4-2} = 2 \times 10^2
\]
Therefore, 4 × 10^4 is 2 × 10^2, or 200 times larger than 2 × 10^2.
**Response:** 200

3. **Estimating the federal debt:**
The federal debt amount of $278,560,125,000 can be approximated as \(2.78560125 × 10^{11}\). For a single-digit approximation, it rounds to \(3 × 10^{11}\).
**Response:** 3 × 10^11

4. **Finding how many times less 10^2 is than 10^6:**
This can be expressed as follows:
\[
\frac{10^6}{10^2} = 10^{6-2} = 10^4
\]
Thus, 10^2 is \(10^{-4}\) times lesser than 10^6.
**Response:** 10(−4)

5. **Expressing the time taken by light in scientific notation:**
The time is given as 0.000000003 seconds, which can be expressed as \(3 \times 10^{-9}\) because we move the decimal point 9 places to the right.
**Response:** 3 × 10(−9)

In summary, the responses are:
1. 0.00000005
2. 200
3. 3 × 10^11
4. 10(−4)
5. 3 × 10(−9)