seconds days and seconds days. Think of some events or phenomena whose time is of the order of: (i) seconds (ii) seconds Write them in scientific notation.

Power Play (Exponents) | IT

Question 46

$10^5$ seconds $\approx 1.16$ days and $10^6$ seconds $\approx 11.57$ days. Think of some events or phenomena whose time is of the order of: (i) $10^5$ seconds (ii) $10^6$ seconds

Write them in scientific notation.

Solution

We will understand the given time durations and find real-world events matching them.

Step 1 — Understanding time durations

We will convert the given time in seconds to days. This helps us understand its duration better. We know 60 seconds make 1 minute. Also, 60 minutes make 1 hour. And 24 hours make 1 day.

So, let us calculate seconds in one day: $1 \text{ day} = 24 \text{ hours} \times 60 \text{ minutes/hour} \times 60 \text{ seconds/minute}$ $= 86400 \text{ seconds}$

The question gives these approximations: $10^5$ seconds $\approx 1.16$ days. $10^6$ seconds $\approx 11.57$ days. These help us find suitable events.

Step 2 — Events for $10^5$ seconds

We need an event lasting about $10^5$ seconds. This is about $100,000$ seconds, or $1.16$ days. A very long train journey, lasting about 1.5 days, is a good example.

Let us calculate the duration of 1.5 days in seconds: $1.5 \text{ days} = 1.5 \times 86400 \text{ seconds}$ $= 129600 \text{ seconds}$

$\boxed{1.296 \times 10^5 \text{ seconds}}$ This value is of the order of $10^5$ seconds. Another example is the time taken for a large project to complete its initial phase.

Step 3 — Events for $10^6$ seconds

We need an event lasting about $10^6$ seconds. This is about $1,000,000$ seconds, or $11.57$ days. A typical school term break fits this. A long holiday trip is also suitable.

Let us consider a holiday trip of 12 days. We will calculate its duration in seconds: $12 \text{ days} = 12 \times 86400 \text{ seconds}$ $= 1036800 \text{ seconds}$

$\boxed{1.0368 \times 10^6 \text{ seconds}}$ This value is very close to $10^6$ seconds. Another example is the time for the Moon to complete about half of its phases.

Answer

(i) Events or phenomena whose time is of the order of $10^5$ seconds: A very long train journey (e.g., 1.5 days): $1.296 \times 10^5$ seconds. The time for a large project's initial phase (e.g., 1.5 days): $1.296 \times 10^5$ seconds.

(ii) Events or phenomena whose time is of the order of $10^6$ seconds: A typical school term break (e.g., 12 days): $1.0368 \times 10^6$ seconds. A long holiday trip (e.g., 12 days): $1.0368 \times 10^6$ seconds.

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Q46

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Write them in scientific notation.

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