Understand that network speeds are measured in bits per second (kilobit,…

The idea

Network speed is a rate: how many bits pass a point each second, written in bits per second (bit/s). The prefixes scale by 1000: 1 kilobit per second (kbit/s) = 1000 bit/s, 1 megabit per second (Mbit/s) = 1000 kbit/s = 1,000,000 bit/s, and 1 gigabit per second (Gbit/s) = 1000 Mbit/s = 1,000,000,000 bit/s. File size is a quantity of bits, so time = file size ÷ transmission rate. Convert units before dividing: 2 MB = 2 × 8 × 1,000,000 = 16,000,000 bits; at 8 Mbit/s, time = 16,000,000 ÷ 8,000,000 = 2 s. Rearranged expressions give file size = rate × time and rate = file size ÷ time. Keep bits and bytes distinct: 1 byte = 8 bits.

What earns the marks

• States that network speed is measured in bits per second (bit/s), with kilobit, megabit and gigabit prefixes scaling by 1000.
• Converts between bit/s, kbit/s, Mbit/s and Gbit/s correctly, e.g. 1 Mbit/s = 1,000,000 bit/s.
• Distinguishes bits from bytes and applies 1 byte = 8 bits when a file size is given in bytes.
• Selects and rearranges the relationship time = file size ÷ transmission rate to find time, file size or rate.
• Carries out a multi-step calculation with consistent units and states the unit of the answer, e.g. seconds.

Common mistakes and how to put them right

• Treating bits and bytes as interchangeable.

  Put it right: A file size in bytes must be multiplied by 8 to give bits before dividing by a rate in bit/s.

• Using 1024 instead of 1000 for kilobit, megabit and gigabit.

  Put it right: These network-speed prefixes scale by powers of 1000.

• Dividing rate by file size instead of file size by rate.

  Put it right: Time = file size ÷ transmission rate, so the larger the rate the smaller the time.

• Forgetting to convert a rate such as 8 Mbit/s into 8,000,000 bit/s before dividing, which gives an answer 1,000,000 times too large.

Exam tips

• Write the formula triangle or equation first: time = file size ÷ rate, file size = rate × time, rate = file size ÷ time.
• Convert every quantity to bits and bit/s before substituting, and show the conversion line so method marks are visible.
• Check the magnitude of the answer: a small file at a fast rate should give a small time, and include the unit (s, bit/s or bits).