how to safely convert from one unit to another

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If you used the same unit to weigh molecules and elephants, your measurements would end up really complicated. The Systeme International d'Unites, called SI units, solves this problem by using prefixes. All prefix multiplies the lowly unit away a sealed power of ten (10, 100, 1000, and so on). This keeps the numbers you're impermanent with manageable, while quickly characteristic the relationship between very large and very small units. Every SI units use the unvaried prefixes, thusly once you acquire them for units of length (metres), you already know how to utilize prefixes for units of Mass (grams),

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Learn the definition of "kilo. " "Kilo" is one of the virtually public unit prefixes, so you might already recognise it from words like-minded "kg" and "kilometre". This prefix means "1000" (one grand). Kilo- is abbreviated As "k-", so a kilogram is "kilo" and a klick is "kilometer".^[1]
2

Convert kilometres to metres. Since kg- means 1 000, one kilometre (km) is isoclinal to 1000 metres (m). Manifold the number of kilometres by 1 000 to get along the same measurement in metres.^[2]

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3

Compare to other units. The base unit does non make any difference in this calculation. American Samoa prospicient as you know the definition of the prefix, you can use the same math to convert between IT and the base unit. Here are a couple examples:
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Find out common larger prefixes. Another common prefix is mega-, which substance one million (1 000 000) and is shortened M. Even larger units use the prefix giga-, which means one trillion (1 000 000 000) and is abbreviated G.^[3] Here are a couple conversions that use these prefixes:
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Convert from a base unit to a larger unit. To win over to a larger unit of measurement of measurement, you'll split up past the conversion factor instead of multiplying. Every bit always, you're less likely to make a mistake if you include the units at each point in your deliberation:^[4]
- 65 300 metres is equal to $65\ 300m*{\frac {1\ km}{1\ 000m}}$ = 65.3 kilometres.
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Learn prefixes with factors inferior than one. What if you want to measure a length shorter than ane measure, or the volume of a cup smaller than one litre? That's when you use prefixes that represent a divide of the base unit. Here are the most common prefixes of this type:^[5]
- centi- (c) means "one centesimal" (0.01). 1 centimetre = 0.01 metres.
- milli- (m) means "one thousandth" (0.001). 1 millimetre = 0.001 metres.
- micro- (µ) means "one millionth" (0.000 001). 1 micrometre = 0.000 001 metres.
- nano- (n) means "one billionth" (0.000 000 001). 1 nanometre = 0.000 000 001 metres.
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Convert between the base unit and smaller units. These conversions bring exactly the same. Just make sure to Seth finished your units so they cancel out, and to keep racetrack of decimals:^[6]
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Check your answer. Probably the most mutual misidentify with these conversions is to accidentally divide instead of multiply or vice versa. There are several ways to catch this slip up:

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1
Get wind the prefixes as powers of ten. All Systeme International prefix represents a different superpowe of ten: 100, 1000, 0.001, and so on. Here are the most informal examples written in scientific notation (standard physique):^[7]
- giga- = 1 000 000 000 = 10⁹
- mega- = 1 000 000 = 10⁶
- kilogram- = 1 000 = 10³
- centi- = 0.01 = 10^-2
- milli- = 0.001 = 10^-3
- micro- = 0.000 001 = 10^-6
- nano- = 0.000 000 001 = 10^-9
- You can also spell a blackbal exponent Eastern Samoa a fraction with a irrefutable exponent in the denominator: $10^{-2}={\frac {1}{10^{2}}}$
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Use knowledge base notation to convert to the base building block. Scientific notation makes it practically easier to convert between units of really divers size. No issue what the final unit you want is, you can start by converting the initial value to the base unit, victimisation scientific annotation.
- Exemplar: How many centimetres are in 13.78 kilometres?
  The answer isn't unmistakable, but you cause know that the kilometer is equal to 10³ metres.
  Therefore, 13.78 km = 13.78 * 10³ metres. You'll use this in the next step.
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Find the changeover to your final unit. Now that you have a fundament unit value (with no more prefix), you can set up an ordinary conversion to the final unit. Write the conversion in powers of ten notational system.
- To continue the example, you know wish to convince 13.78 * 10³ metres into centimetres.
  The prefix centi- substance 10^-2, so there is ${\frac {1cm}{10^{-2}m}}$
4
Prepare the conversion as a single expression. Arrange your conversion victimization power of 10 note for every values. This gives you a fraction that divides one power of ten by another:
- $13.78*10^{3}m*{\frac {1cm}{10^{-2}m}}={\frac {13.78*10^{3}}{10^{-2}}}\$ Cm
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Simplify the exponents. To divide one mathematical notation expression by the some other (when they some possess the homophonic base), take the top advocate and subtract the bottom exponent. The answer is the new exponent in your answer, with the same base (which is forever 10 in these transition problems).^[8]
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Simplify the formula. Once you are cosy with this process, you crapper combine the undiversified process into a pair quick steps:

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Question

What's the velocity of a auto in kph if IT travels 16 km in 13 minutes?

Divide 60 minutes by 13 minutes. That's 4.615. Procreate that away 16 km: (4.615)(16 kilometre) = 73.84 km. That means that if a car travels 16 klick in 13 proceedings, at the similar hotfoot it would travel 73.84 km in one hour. The car is traveling at 73.84 kph.

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Reference Guide

The bold rows represent the most common prefixes.

yotta | 10²⁴ | Y | 1,000,000,000,000,000,000,000,000 base units
zetta | 10²¹ | Z | 1,000,000,000,000,000,000,000
exa | 10¹⁸ | E | 1,000,000,000,000,000,000
peta | 10¹⁵ | P | 1,000,000,000,000,000
tera | 10¹² | T | 1,000,000,000,000
giga | 10⁹ | G | 1,000,000,000
mega | 10⁶ | M | 1,000,000
kilo | 10³ | k | 1,000
hecto | 10² | h | 100
deka | 10¹ | district attorney | 10
(zero prefix) | 10⁰ | | 1 base social unit
deci | 10^-1 | d | 0.1
centi | 10^-2 | c | 0.01
milli | 10^-3 | m | 0.001
micro | 10^-6 | µ | 0.000001
nano | 10^-9 | n | 0.000000001
pico | 10^-12 | p | 0.000000000001
femto | 10^-15 | f | 0.000000000000001
atto | 10^-18 | a | 0.000000000000000001
zepto | 10^-21 | z | 0.000000000000000000001
yocto | 10^-24 | y | 0.000000000000000000000001 base units

metre (length) (m)
litre (volume) (L)
Gram (mass/weight) (g)
joule (heat/get-up-and-go) (J)
coulomb (accuse) (C)
James Watt (business leader) (W)
volt (electrical voltage) (V)
hertz (relative frequency) (Hz)
newton (force) (N)
pascal (imperativeness) (Keystone State)
seconds (sentence) (s)

These units are almost always seen in their base form, only they rump utilize SI prefixes.

moles (number of tactful particles in a sample) (mol)
kelvins (temperature) (K)
degrees Celsius (temperature) (ºC)
amperes (electrical prevalent) (A)
cd (luminous intensity) (cd)

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You probably don't need to memorize prefixes larger than giga- surgery smaller than nano-. Those are seldom used except in specific William Claude Dukenfield of bailiwick.

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Remember which "direction" you are going! Check your answers against reality, if possible.
You can but use this method acting if the base units are the same. Converting between kilograms and pounds, e.g., requires a divergent chemical formula.

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