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


0.00000005
0.0000000053
0.00000006
0.0000005

9 answers

To express the radius of a hydrogen atom, which is \( 0.0000000529177 \) mm, as an approximation, we can round it to a more manageable number.

The number \( 0.0000000529177 \) is approximately \( 0.000000053 \) when rounded to two significant figures, which is also equivalent to \( 0.00000005 \).

Among the choices provided:

  • \( 0.00000005 \)
  • \( 0.0000000053 \)
  • \( 0.00000006 \)
  • \( 0.0000005 \)

The best approximation from this list is \( 0.00000005 \).

Therefore, the correct response is:

0.00000005.

How many times is 4 × 10 x 10 x 10 x10 larger than 2 × 10 x 10 ?(1 point) Responses 200 200 2,000 2,000 2 2 20

Let's first express the two quantities clearly:

  1. \( 4 \times 10 \times 10 \times 10 \times 10 \) can be rewritten in scientific notation as: \[ 4 \times 10^4 \]

  2. \( 2 \times 10 \times 10 \) can be rewritten as: \[ 2 \times 10^2 \]

Next, we need to find how many times \( 4 \times 10^4 \) is larger than \( 2 \times 10^2 \). We can do this by dividing \( 4 \times 10^4 \) by \( 2 \times 10^2 \):

\[ \frac{4 \times 10^4}{2 \times 10^2} = \frac{4}{2} \times \frac{10^4}{10^2} = 2 \times 10^{4-2} = 2 \times 10^2 = 2 \times 100 = 200 \]

Therefore, \( 4 \times 10^4 \) is 200 times larger than \( 2 \times 10^2 \).

The correct response is:

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)

To estimate the federal debt of Country C, which is $278,560,125,000, we can express it in a form that is easier to work with: a single digit times an integer power of 10.

First, we can round $278,560,125,000 to the nearest billion for a quick estimation.

The value can be expressed as:

  1. Magnitude: The number is in the hundreds of billions, indicated by the first few digits.
  2. Round off: We see that \( 278 \) billion is approximately \( 300 \) billion when rounded.

In scientific notation, \( 300 \) billion can be expressed as: \[ 3.0 \times 10^{11} \]

Therefore, the closest estimation of the amount in the form of a single digit times an integer power of 10 is:

\[ 3 \times 10^{11} \]

So the final answer is:

3 × 10^11.

How many times less is 10 x 10 than 10 x 10 x 10 x 10 x 10 x 10? Express your answer as an integer power of 10.(1 point) Responses 10−4 10 superscript negative 4 baseline 10,000 10,000 104 10 superscript 4 baseline 0.0001

To determine how many times less \( 10 \times 10 \) is than \( 10 \times 10 \times 10 \times 10 \times 10 \times 10 \), we can start by simplifying each expression.

  1. Calculate \( 10 \times 10 \): \[ 10 \times 10 = 10^2 \]

  2. Calculate \( 10 \times 10 \times 10 \times 10 \times 10 \times 10 \): \[ 10 \times 10 \times 10 \times 10 \times 10 \times 10 = 10^6 \]

Now we need to find how many times less \( 10^2 \) is than \( 10^6 \), which can be calculated by dividing \( 10^2 \) by \( 10^6 \):

\[ \frac{10^2}{10^6} = 10^{2-6} = 10^{-4} \]

Thus, \( 10 \times 10 \) is \( 10^{-4} \) times less than \( 10 \times 10 \times 10 \times 10 \times 10 \times 10 \).

The correct response is:

10^{-4}.

write it regulrally

Certainly! The answer in regular notation is:

0.0001.

This means that \( 10 \times 10 \) is \( 0.0001 \) times less than \( 10 \times 10 \times 10 \times 10 \times 10 \times 10 \).