Do you wonder how people figured out that the Earth completes one revolution around the Sun in exactly 364.2422 days?

Question

Homi · Accepted Answer

We will use decimal operations to understand the Earth's revolution period.

Step 1 — Rounding the revolution period

The Earth takes 364.2422 days for one revolution. We need to round this number to the nearest hundredth. The hundredths place is the second digit after the decimal point. We look at the digit in the thousandths place. This digit is 2. Since 2 is less than 5, we keep the hundredths digit as it is.

$364.2422 \approx 364.24$

$\boxed{364.24 \text{ days}}$

Diagram 1

Step 2 — Converting the decimal part to hours, minutes, seconds

The full days are 364. The decimal part is 0.2422 days. Let us convert this decimal part into hours. There are 24 hours in one day. So, we multiply the decimal part by 24.

$0.2422 \times 24$ $= 5.8128$

$\boxed{5.8128 \text{ hours}}$

Now, we have 5 full hours. The decimal part of the hours is 0.8128 hours. Let us convert this decimal part into minutes. There are 60 minutes in one hour. So, we multiply the decimal part by 60.

$0.8128 \times 60$ $= 48.768$

$\boxed{48.768 \text{ minutes}}$

Now, we have 48 full minutes. The decimal part of the minutes is 0.768 minutes. Let us convert this decimal part into seconds. There are 60 seconds in one minute. So, we multiply the decimal part by 60.

$0.768 \times 60$ $= 46.08$

$\boxed{46.08 \text{ seconds}}$

So, the decimal part is 5 hours, 48 minutes, and approximately 46 seconds.

Step 3 — Calculating calendar difference over 10 years

The Earth's revolution is 364.2422 days. A calendar year is exactly 364 days. Let us find the difference for one year. We subtract the calendar year from the actual revolution period.

$364.2422 - 364$ $= 0.2422$

$\boxed{0.2422 \text{ days}}$

This is the amount the calendar falls behind each year. We need to find the total difference after 10 years. So, we multiply the yearly difference by 10.

$0.2422 \times 10$ $= 2.422$

$\boxed{2.422 \text{ days}}$

After 10 years, the calendar would be behind by 2.422 days.

Answer

(i) The revolution period rounded to the nearest hundredth is 364.24 days. (ii) The decimal part is 5 hours, 48 minutes, and 46.08 seconds. (iii) After 10 years, the calendar would be behind by 2.422 days.

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