Let's address each question one by one.
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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
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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
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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
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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)
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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:
- 0.00000005
- 200
- 3 × 10^11
- 10(−4)
- 3 × 10(−9)