Megabits per day to Tebibytes per hour conversion

How to convert megabits per day to tebibytes per hour?

To convert 1 Megabit per day (Mbps/day) to Tebibytes per hour (TiB/h), follow these steps for both base 10 (decimal) and base 2 (binary) cases.

Base 10 (Decimal) Calculation:

1. Convert Megabits per day to Megabits per hour:

   • There are 24 hours in a day. $\frac{1 \text{ Megabit}}{1 \text{ day}} \times \frac{1 \text{ day}}{24 \text{ hours}} = \frac{1}{24} \text{ Megabits per hour}$

2. Convert Megabits to Bits:

   • There are $10^6$ bits in 1 Megabit (base 10). $\frac{1}{24} \text{ Megabits per hour} \times 10^6 \text{ bits per Megabit} = \frac{10^6}{24} \text{ bits per hour}$

3. Convert Bits to Tebibytes:

   • There are $8 \times 10^12$ bits in 1 Tebibyte (base 10, traditionally used decimal Terabyte TB for simplicity in calculations). $\frac{10^6}{24} \text{ bits per hour} \times \frac{1 \text{ Tebibyte}}{8 \times 10^{12} \text{ bits}} = \frac{10^6}{24 \times 8 \times 10^{12}} \text{ Tebibytes per hour}$ $= \frac{10^6}{192 \times 10^{12}} \text{ Tebibytes per hour}$ $= \frac{1}{192 \times 10^6} \text{ Tebibytes per hour}$ $≈ 5.208 \times 10^{-9} \text{ Tebibytes per hour}$

Base 2 (Binary) Calculation:

1. Convert Megabits per day to Megabits per hour:

   • This conversion step remains the same: $\frac{1 \text{ Megabit}}{1 \text{ day}} \times \frac{1 \text{ day}}{24 \text{ hours}} = \frac{1}{24} \text{ Megabits per hour}$

2. Convert Megabits to Bits:

   • There are $2^{20}$ (1,048,576) bits in 1 Megabit (base 2). $\frac{1}{24} \text{ Megabits per hour} \times 1,048,576 \text{ bits per Megabit} = \frac{1,048,576}{24} \text{ bits per hour}$

3. Convert Bits to Tebibytes:

   • There are $2^{43}$ (8,796,093,022,208) bits in 1 Tebibyte (base 2). $\frac{1,048,576}{24} \text{ bits per hour} \times \frac{1 \text{ Tebibyte}}{8,796,093,022,208 \text{ bits}} = \frac{1,048,576}{24 \times 8,796,093,022,208} \text{ Tebibytes per hour}$ $= \frac{1,048,576}{211,105,232,532,992} \text{ Tebibytes per hour}$ $≈ 4.970 \times 10^{-9} \text{ Tebibytes per hour}$

Real-World Examples (other quantities of Megabits per day):

1. Example: 100 Megabits per day

   • Base 10: $100 \text{ Megabits per day} \approx 5.208 \times 10^{-7} \text{ Tebibytes per hour}$
   • Base 2: $100 \text{ Megabits per day} ≈ 4.970 \times 10^{-7} \text{ Tebibytes per hour}$

2. Example: 10,000 Megabits per day

   • Base 10: $10,000 \text{ Megabits per day} ≈ 5.208 \times 10^{-5} \text{ Tebibytes per hour}$
   • Base 2: $10,000 \text{ Megabits per day} ≈ 4.970 \times 10^{-5} \text{ Tebibytes per hour}$

3. Example: 1 Terabit per day (1,000,000 Megabits per day)

   • Base 10: $1,000,000 \text{ Megabits per day} ≈ 5.208 \times 10^{-3} \text{ Tebibytes per hour}$
   • Base 2: $1,000,000 \text{ Megabits per day} ≈ 4.970 \times 10^{-3} \text{ Tebibytes per hour}$

Always specify whether you are using base 10 or base 2 in any technical documentation, as it affects the conversion results.