Cm To Meters Scientific Notation

3.three: Scientific Notation

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How far is the Sun from Earth?

Astronomers are accepted to very large numbers. While the moon is simply \(406,697 \: \text{km}\) from globe at its maximum distance, the sun is much further abroad \(\left( 150 \: \text{million km} \right)\). Proxima Centauri, the star nearest the earth, is \(39,900,000,000,000 \: \text{km}\) away—and this is simply the kickoff of long distances. On the other stop of the calibration, some biologists deal with very small numbers: a typical fungus could be as small equally 30 micrometers \(\left( 0.000030 \: \text{meters} \right)\) in length, and a virus might only exist 0.03 micrometers \(\left( 0.00000003 \: \text{meters} \right)\) long.

Scientific Notation

Scientific notation is a style to express numbers equally the product of two numbers: a coefficient and the number ten raised to a power. Information technology is a very useful tool for working with numbers that are either very big or very small. Every bit an example, the distance from World to the Sun is about 150,000,000,000 meters—a very large distance indeed. In scientific notation, the distance is written as \(1.v \times 10^{11} \: \text{m}\). The coefficient is the i.5 and must be a number greater than or equal to 1, and less than ten. The power of ten, or exponent, is eleven because you lot would accept to multiply 1.5 by \(ten^{11}\) to get the correct number. Scientific notation is sometimes referred as exponential notation. A summary of SI units is given in the table below.

Table \(\PageIndex{one}\): SI Prefixes
Prefix	Unit of measurement Abridgement	Exponential Factor	Significant	Case
giga	\(\text{One thousand}\)	\(10^9\)	1,000,000,000	1 gigameter \(\left( \text{Gm} \right) = 10^9 \: \text{1000}\)
mega	\(\text{M}\)	\(10^six\)	1,000,000	1 megameter \(\left( \text{Mm} \right) = 10^six \: \text{m}\)
kilo	\(\text{one thousand}\)	\(10^3\)	one,000	1 kilometer \(\left( \text{km} \right) = 1,000 \: \text{thou}\)
hecto	\(\text{h}\)	\(x^2\)	100	ane hectometer \(\left( \text{hm} \right) = 100 \: \text{g}\)
deka	\(\text{da}\)	\(10^1\)	ten	one dekameter \(\left( \text{dam} \right) = ten \: \text{m}\)
		\(10^0\)	1	1 meter \(\left( \text{m} \correct)\)
deci	\(\text{d}\)	\(10^{-1}\)	ane/ten	1 decimeter \(\left( \text{dm} \right) = 0.1 \: \text{m}\)
centi	\(\text{c}\)	\(10^{-2}\)	ane/100	one centimeter \(\left( \text{cm} \right) = 0.01 \: \text{m}\)
milli	\(\text{m}\)	\(10^{-3}\)	i/one,000	1 millimeter \(\left( \text{mm} \right) = 0.001 \: \text{thou}\)
micro	\(\mu\)	\(10^{-6}\)	1/1,000,000	1 micrometer \(\left( \mu \text{thou} \right) = 10^{-6} \: \text{grand}\)
nano	\(\text{n}\)	\(ten^{-ix}\)	1/one,000,000,000	i nanometer \(\left( \text{nm} \right) = 10^{-ix} \: \text{m}\)
pico	\(\text{p}\)	\(10^{-12}\)	1/1,000,000,000,000	1 picometer \(\left( \text{pm} \correct) = ten^{-12} \: \text{thou}\)

When working with small numbers, nosotros apply a negative exponent. And then 0.i meters is \(1 \times 10^{-ane}\) meters, 0.01 is \(1 \times 10^{-two}\) and so forth. The table in a higher place gives examples of smaller units. Note the use of the leading zero (the aught to the left of the decimal point). That digit is there to help you lot see the decimal betoken more clearly. The figure 0.01 is less likely to exist misunderstood than .01, where you may not meet the decimal.

Summary

Scientific notation allows us to limited very large or very small numbers in a convenient way.
Scientific note uses a coefficient (a number between 1 and 10) and a power of ten sufficient for the actual number.

Review

What is scientific note?
What do we utilise scientific annotation for?
What is a leading zero?
Express 150,000,000 in scientific notation.
Limited 0.000043 in scientific notation.