Converting Unit

Key Stage 3

Meaning

Converting units is when one unit prefix is switched for another.

About Converting Units

The Unit Prefixes are:

• kilo (k) - 1000 times bigger.
• centi (c) - 100 times smaller.
• milli (m) - 1000 times smaller.
• micro (µ) - 1000,000 times smaller.

Kilo

To convert from kilo to the base unit you must times by 1000. \[5km = 5 \times 1000m = 5000m\] \[12kA = 12\times1000A = 12000A\] \[3.4kV = 3.4\times1000V = 3400V\] \[0.53kN = 0.53\times1000N = 530N\] \[0.082kJ = 0.082\times1000J = 82J\]

To convert to kilo from a base unit you must divide by 1000. \[23000m = \frac{23000}{1000}km = 23km\]

\[8200A = \frac{8200}{1000}kA = 8.2kA\]

\[670V = \frac{670}{1000}kV = 0.67kV\]

\[32N = \frac{32}{1000}kN = 0.032kN\]

\[2J = \frac{2}{1000}kJ = 0.002kJ\]

Centi

To convert from centi to the base unit you must divide by 100. \[63000cm = \frac{63000}{100}m = 630m\] \[3500cm = \frac{3500}{100}m = 35m\] \[940cm = \frac{940}{100}m = 9.4m\] \[93cm = \frac{93}{100}m = 0.93m\] \[4cm = \frac{4}{100}m = 0.02m\]

To convert to centi from a base unit you must times by 100. \[7m = 7\times100cm = 700cm\]

\[15m = 15 \times 100cm = 1500cm\]

\[8.2m = 8.2\times100cm = 820cm\]

\[0.26m = 0.26\times100cm = 260cm\]

\[0.03m = 0.03\times100cm = 3cm\]

Milli

To convert from milli to the base unit you must divide by 1000. \[83000mm = \frac{83000}{1000}m = 83m\]

\[2600mA = \frac{2600}{1000}A = 2.6A\]

\[170mV = \frac{170}{1000}V = 0.17V\]

\[22mN = \frac{22}{1000}N = 0.022N\]

\[6mJ = \frac{6}{1000}J = 0.006J\]

To convert to milli from a base unit you must times by 1000. \[4m = 4\times1000mm = 4000mm\]

\[34A = 34\times1000mA = 24000mA\]

\[1.9V = 1.9\times1000mV = 1900mV\]

\[0.73N = 0.73\times1000mN = 730mN\]

\[0.092J = 0.092\times1000mJ = 92mJ\]

Micro

To convert from micro to the base unit you must divide by 1000,000. \[63000\mu m = \frac{63000}{1000,000}m = 0.063m\]

\[8400\mu m = \frac{8400}{1000,000}m = 0.0084m\]

\[260\mu m = \frac{260}{1000,000}m = 0.00026m\]

\[98\mu m = \frac{98}{1000,000}m = 0.000098m\]

\[3\mu m = \frac{3}{1000,000}m = 0.000003m\]

To convert to micro from a base unit you must times by 1000,000. \[8m = 8\times1000,000 \mu m = 8,000,000\mu m\]

\[54m = 54\times1000,000 \mu m = 24,000,000\mu m\]

\[6.2m = 6.2\times1000,000 \mu m = 6,200,000\mu m\]

\[0.33m = 0.33\times1000,000 \mu m = 330,000\mu m\]

\[0.052m = 0.052\times1000,000 \mu m = 52,000\mu m\]

Key Stage 4

Meaning

Converting units is when one unit prefix is switched for another.

About Converting Units

The Unit Prefixes are:

• mega (M) - 1000,000 times bigger.
• kilo (k) - 1000 times bigger.
• deci (d) - 10 times smaller.
• centi (c) - 100 times smaller.
• milli (m) - 1000 times smaller.
• micro (µ) - 1,000,000 times smaller.
• nano (n) - 1,000,000,000 times smaller.

Mega

To convert from mega to the base unit you must times by 10⁶. \[5Mm = 5 \times 10^6m = 5000,000m\] \[12MA = 12\times 10^6A = 12,000,000A\] \[3.4MV = 3.4\times 10^6V = 3,400,000V\] \[0.53MN = 0.53\times 10^6N = 530,000N\] \[0.082MJ = 0.082\times 10^6J = 82,000J\]

To convert to mega from a base unit you must divide by 10⁶. \[23000m = \frac{23000}{10^6}Mm = 0.023Mm\]

\[8200A = \frac{8200}{10^6}MA = 0.0082MA\]

\[670V = \frac{670}{10^6}MV = 0.00067MV\]

\[32N = \frac{32}{10^6}MN = 0.000032MN\]

\[2J = \frac{2}{10^6}MJ = 0.000002MJ\]

Kilo

To convert from kilo to the base unit you must times by 10³. \[5km = 5 \times 10^3m = 5000m\] \[12kA = 12\times 10^3A = 12000A\] \[3.4kV = 3.4\times 10^3V = 3400V\] \[0.53kN = 0.53\times 10^3N = 530N\] \[0.082kJ = 0.082\times 10^3J = 82J\]

To convert to kilo from a base unit you must divide by 10³. \[23000m = \frac{23000}{10^3}km = 23km\]

\[8200A = \frac{8200}{10^3}kA = 8.2kA\]

\[670V = \frac{670}{10^3}kV = 0.67kV\]

\[32N = \frac{32}{10^3}kN = 0.032kN\]

\[2J = \frac{2}{10^3}kJ = 0.002kJ\]

Deci

To convert from deci to the base unit you must times by 10^-1. \[63000dm = 63000 \times 10^{-1}m = 630m\]

\[3500dm = 3500\times10^{-1}m = 350m\]

\[940dm = 940\times10^{-1}m = 94m\]

\[93dm = 93\times10^{-1}m = 9.3m\]

\[4dm = 4\times10^{-1}m = 0.2m\]

To convert to deci from a base unit you must times by 10¹ because there are 10 of them in the base unit. \[7m = 7\times10^{1}cm = 700cm\]

\[15m = 15\times10^{1}dm = 150dm\]

\[8.2m = 8.2\times10^{1}dm = 82dm\]

\[0.26m = 0.26\times10^{1}dm = 2.6dm\]

\[0.03m = 0.03\times10^{1}dm = 0.3dm\]

Centi

To convert from centi to the base unit you must times by 10^-2. \[63000cm = 63000 \times 10^{-2}m = 630m\] \[3500cm = 3500\times10^{-2}m = 35m\] \[940cm = 940\times10^{-2}m = 9.4m\] \[93cm = 93\times10^{-2}m = 0.93m\] \[4cm = 4\times10^{-2}m = 0.02m\]

To convert to centi from a base unit you must times by 10² because there are 100 of them in the base unit. \[7m = 7\times10^{2}cm = 700cm\]

\[15m = 15\times10^{2}cm = 1500cm\]

\[8.2m = 8.2\times10^{2}cm = 820cm\]

\[0.26m = 0.26\times10^{2}cm = 260cm\]

\[0.03m = 0.03\times10^{2}cm = 3cm\]

Milli

To convert from milli to the base unit you must times by 10^-3. \[83000mm = 83000\times10^{-3}m = 83m\]

\[2600mA = 2600\times10^{-3}A = 2.6A\]

\[170mV = 170\times10^{-3}V = 0.17V\]

\[22mN = 22\times10^{-3}N = 0.022N\]

\[6mJ = 6\times10^{-3}J = 0.006J\]

To convert to milli from a base unit you must times by 10³ because there are 1000 of them in the base unit. \[4m = 4}{10^{3}mm = 4000mm\]

\[34A = 34\times10^{3}mA = 24000mA\]

\[1.9V = 1.9\times10^{3}mV = 1900mV\]

\[0.73N = 0.73\times10^{3}mN = 730mN\]

\[0.092J = 0.092\times10^{3}mJ = 92mJ\]

Micro

To convert from micro to the base unit you must times by 10^-6. \[63000\mu m = 63000\times10^{-6}m = 0.063m\]

\[8400\mu m = 8400\times10^{-6}m = 0.0084m\]

\[260\mu m = 260\times10^{-6}m = 0.00026m\]

\[98\mu m = 98\times10^{-6}m = 0.000098m\]

\[3\mu m = 3\times10^{-6}m = 0.000003m\]

To convert to micro from a base unit you must times by 10⁶ because there are 1,000,000 of them in the base unit. \[8m = 8\times10^{6} \mu m = 8,000,000\mu m\]

\[54m = 54\times10^{6} \mu m = 24,000,000\mu m\]

\[6.2m = 6.2\times10^{6} \mu m = 6,200,000\mu m\]

\[0.33m = 0.33\times10^{6} \mu m = 330,000\mu m\]

\[0.052m = 0.052\times10^{6} \mu m = 52,000\mu m\]

Nano

To convert from nano to the base unit you must times by 10^-9. \[63000nm = 63000\times10^{-9}m = 0.000063m\]

\[8400nA = 8400\times10^{-9}A = 0.0000084A\]

\[260nV = 260\times10^{-9}V = 0.00000026V\]

\[98nN = 98\times10^{-9}N = 0.000000098N\]

\[3nJ = 3\times10^{-9}J = 0.000000003J\]

To convert to nano from a base unit you must times by 10⁹ because there are 1,000,000,000 of them in the base unit. \[8m = 8\times10^{9} nm = 8,000,000,000nm\]

\[54A = 54\times10^{9} nA = 24,000,000,000nA\]

\[6.2V = 6.2\times10^{9} nV = 6,200,000,000nV\]

\[0.33N = 0.33\times10^{9} nN = 330,000,000nN\]

\[0.052J = 0.052\times10^{9} nJ = 52,000,000nJ\]

References

Edexcel

Converting units, pages 19, 20, 32, GCSE Biology, CGP, Edexcel

Converting units, pages 8, 14, GCSE Combined Science; The Revision Guide, CGP, Edexcel

Converting units, pages 9, 15, GCSE Biology; The Revision Guide, CGP, Edexcel

OCR

Converting units, pages 8, 158, Gateway GCSE Combined Science; The Revision Guide, CGP, OCR