Megabits per hour to Gigabits per day conversion

How to convert megabits per hour to gigabits per day?

Certainly! Let's step through how to convert 1 Megabit per hour (Mb/hr) to Gigabits per day (Gb/day).

Base 10 (Decimal)

In base 10 (also called the decimal system):

1. Convert hours to days: $1 \text{ hour} = \frac{1}{24} \text{ day}$ So, if you have a data rate of 1 Mb/hr, in one day (which is 24 hours), the total data transfer is: $1 \text{ Mb/hr} \times 24 \text{ hours/day} = 24 \text{ Mb/day}$

2. Convert Megabits to Gigabits: 1 Gigabit (Gb) = 1,000 Megabits (Mb) in base 10. $24 \text{ Mb/day} \times \frac{1 \text{ Gb}}{1,000 \text{ Mb}} = 0.024 \text{ Gb/day}$

So, in base 10: $1 \text{ Mb/hr} = 0.024 \text{ Gb/day}$

Base 2 (Binary)

In base 2 (also called the binary system):

1. Convert hours to days: This step remains the same as in base 10. $1 \text{ Mb/hr} \times 24 \text{ hours/day} = 24 \text{ Mb/day}$

2. Convert Megabits to Gigabits: 1 Gigabit (Gb) = 1,024 Megabits (Mb) in base 2. $24 \text{ Mb/day} \times \frac{1 \text{ Gb}}{1,024 \text{ Mb}} = 0.0234375 \text{ Gb/day}$

So, in base 2: $1 \text{ Mb/hr} = 0.0234375 \text{ Gb/day}$

Real-World Examples

1. Internet Speed:

   • A typical home internet connection might have a download speed of, say, 50 Megabits per second (Mb/s). To convert this to Megabits per hour: $50 \text{ Mb/s} \times 60 \text{ seconds/minute} \times 60 \text{ minutes/hour} = 180,000 \text{ Mb/hr}$

     • How many Gigabits per day is this in base 10? $180,000 \text{ Mb/hr} \times 24 \text{ hours/day} \times \frac{1 \text{ Gb}}{1,000 \text{ Mb}} = 4,320 \text{ Gb/day}$

     • In base 2: $180,000 \text{ Mb/hr} \times 24 \text{ hours/day} \times \frac{1 \text{ Gb}}{1,024 \text{ Mb}} \approx 4,101.5625 \text{ Gb/day}$

2. Streaming Video:

   • Netflix might stream video at a rate of about 5 Megabits per second (Mb/s) for high-definition video. To convert this to Megabits per hour: $5 \text{ Mb/s} \times 60 \text{ seconds/minute} \times 60 \text{ minutes/hour} = 18,000 \text{ Mb/hr}$

     • How many Gigabits per day is this in base 10? $18,000 \text{ Mb/hr} \times 24 \text{ hours/day} \times \frac{1 \text{ Gb}}{1,000 \text{ Mb}} = 432 \text{ Gb/day}$

     • In base 2: $18,000 \text{ Mb/hr} \times 24 \text{ hours/day} \times \frac{1 \text{ Gb}}{1,024 \text{ Mb}} \approx 421.875 \text{ Gb/day}$

These conversions can be useful for understanding the data usage patterns for different technologies and activities over a given time frame.