Q: Convert 18 months to years

The correct answer is: $1.5\text{ years}$ Explanation To convert months to years, divide the number of months by 12 because there are 12 months in a year. Eighteen months is one and a half years. Steps: Write the conversion: $$18\text{ months} = \frac{18}{12}\text{ years}$$ Simplify the fraction: $$\frac{18}{12} = \frac{3}{2}$$ Convert to decimal: $$\frac{3}{2} = 1.5$$ Therefore, $18\text{ months} = 1.5\text{ years}$.

Q: How many minutes are there in exactly one week?

The correct answer is: $10080$ minutes Explanation One week has 7 days. Each day has 24 hours and each hour has 60 minutes, so multiply those factors to get the total minutes in a week. Steps: Number of hours in one day: $$1\text{ day}=24\text{ h}$$ Number of minutes in one hour: $$1\text{ h}=60\text{ min}$$ Multiply to get minutes in 7 days: $$7\text{ days}\times24\text{ h/day}\times60\text{ min/h}=10080\text{ min}$$ Therefore, there are $10080$ minutes in exactly one week.

Q: How many day are in 72hours

The correct answer is: 3 days Explanation A day has 24 hours. To find how many days are in 72 hours, divide the total hours by the number of hours per day. Steps: $1\text{ day} = 24\text{ hours}$ $72 \div 24 = 3$ $72\text{ hours} = 3\text{ days}$ Therefore, 72 hours equals 3 days.

Question

How many days will the year 2100 have

Accepted Answer

The correct answer is: $365$

Explanation

In the Gregorian calendar, a year is a leap year (366 days) if it is divisible by $4$, except that years divisible by $100$ are not leap years unless they are also divisible by $400$. Year $2100$ is a century year, so we must apply the century rule.

Steps:

Check divisibility by $4$: $$2100 \div 4 = 525\quad	ext{(integer)}$$
Because it's divisible by $100$, apply the century exception: $$2100 \div 100 = 21\quad	ext{(century year)}$$
Check divisibility by $400$: $$2100 \div 400 = 5.25\quad	ext{(not an integer)}$$

Equivalently, $$2100 = 400	imes5 + 100\quad	ext{(remainder }100	ext{)}$$

Since $2100$ is not divisible by $400$, it is not a leap year under the Gregorian rule. Therefore, year $2100$ will have $365$ days.

Note: Under the Julian calendar (which treats every year divisible by $4$ as a leap year), $2100$ would be a leap year (366 days). The modern civil calendar is Gregorian, so use 365 days.