Scientific notation is used to turn small or large inconvenient numbers into manageable ones.

Concept #1: Understanding Scientific Notation

A scientific notation value is comprised of 3 parts: the **coefficient**, **base** and **exponent**.

Example #1: Convert the following numbers into scientific notation.

Write the following number in scientific notation and round off to three significant figures: 31152 x 10-15 .

Write the following number in scientific notation and round off to five significant figures: 0.00392708 x 10 81 .
a) 3.9271 x 10 84
b) 3.9270 x 10 78
c) 0.39271 x 10 78
d) 3.9270 x 10 80
e) 3.9271 x 10 78

Use scientific notation to express each quantity with only the base units (no prefix multipliers).
b. 18 fs

Use scientific notation to express each quantity with only the base units (no prefix multipliers).
c. 128 pm

Use scientific notation to express each quantity with only the base units (no prefix multipliers).
d. 35 µm

The Vehicle Assembly Building at the John F. Kennedy Space Center in Cape Canaveral, Florida, is the largest building in the world, with a volume of 3,666,500 m3.Express this volume in scientific notation.

The average thickness of a human hair is about 100 microns (m).Write it in scientific notation.

The average thickness of a human hair is about 100 microns (m).Write it without scientific notation.

Express the diameter of an insulin molecule, 0.000 000 005
m, in scientific notation.

Express the circumference of the Earth at the Equator, 40,075,017
m, in scientific notation.

Express the following quantities in scientific notation using fundamental SI units of mass and length given in the table below.
The Seven Fundamental SI Units of Measure
Physical Quantity
Name of Unit
Abbreviation
Mass
kilogram
kg
Length
meter
m
Temperature
kelvin
K
Amount of substance
mole
mol
Time
second
s
Electric current
ampere
A
Luminous intensity
candela
cd
The mass of carbon dioxide emitted from a large power plant each year, 20
Tg.

Express the following number in scientific notation 0.000275 _____________________
How many significant figures in your answer _______________

The circumference of Earth through the poles is 40,008 km. Round this number to four significant figures, and express it in standard exponential notation.

Use scientific notation to express each quantity with only the base units (no prefix multipliers). a. 4.5 ns

Convert the following measurements from scientific notation to standard notation: 3.221 x 10-3 mm

Convert the following measurements from scientific notation to standard notation: 8.940 x 105 m

Convert the following measurements from scientific notation to standard notation: 1.35082 x 10-12 m3

Convert the following measurements from scientific notation to standard notation: 6.4100 x 102 km

Write the following number in scientific notation: 0.00047

Write the following number in scientific notation: 210,006

Write the following number in scientific notation: 2160.5

Write the following number in scientific notation: 0.0380

Write the following number in scientific notation: 4270.8

Write the following number in scientific notation: 58,200.9

Write the following number in standard notation. Use a terminal decimal point when needed.1.0070 x 104

Write the following number in standard notation. Use a terminal decimal point when needed.8.85 x 10−7

Write the following number in standard notation. Use a terminal decimal point when needed.3.004 x 10−3

Write the following number in standard notation. Use a terminal decimal point when needed.3.46 x 10−5

Write the following number in standard notation. Use a terminal decimal point when needed.7.5 x 102

Write the following number in standard notation. Use a terminal decimal point when needed.1.8856 x 102

Convert the following into correct scientific notation: 802.5 x 10 2

Convert the following into correct scientific notation: 1009.8 x 10 −6

Convert the following into correct scientific notation: 0.077 x 10 −9

Convert the following into correct scientific notation: 14.3 x 10 1

Convert the following into correct scientific notation: 851 x 10 −2

Convert the following into correct scientific notation: 7500 x 10 −3

Express the following quantities in scientific notation using fundamental SI units of mass and length given in the table below.The Seven Fundamental SI Units of MeasurePhysical QuantityName of UnitAbbreviationMasskilogramkgLengthmetermTemperaturekelvinKAmount of substancemolemolTimesecondsElectric currentampereALuminous intensitycandelacdThe diameter of a human hair, 70 µm.

Write the following number in scientific notation: 131,000.0

Write the following number in scientific notation: 282.0

Write the following number in standard notation. Use a terminal decimal point when needed.5.55 x 103

Write the following number in standard notation. Use a terminal decimal point when needed.6.500 x 103

Express each of the following numbers in exponential notation with correct significant figures:(a) 704

Express each of the following numbers in scientific notation with correct significant figures:(b) 0.239

Express each of the following numbers in scientific notation with correct significant figures:(c) 90743

Express each of the following numbers in scientific notation with correct significant figures:(d) 134.2

Express each of the following numbers in scientific notation with correct significant figures:(e) 0.05499

Express each of the following numbers in scientific notation with correct significant figures:(f) 10000.0

Express each of the following numbers in scientific notation with correct significant figures:(g) 0.000000738592

Express each of the following numbers in exponential notation with correct significant figures:(b) 0.03344

Express each of the following numbers in exponential notation with correct significant figures:(c) 547.9

Express each of the following numbers in exponential notation with correct significant figures:(d) 22086

Express each of the following numbers in exponential notation with correct significant figures:(e) 1000.00

Express each of the following numbers in exponential notation with correct significant figures:(f) 0.0000000651

Express each of the following numbers in exponential notation with correct significant figures:(g) 0.007157

Express each of the following numbers in scientific notation with correct significant figures:(a) 711.0