36
Scientific Notation
Scientific notation is used to express extremely large or extremely small numbers efficiently.
The main idea is to write the number you want as a number between 1 and 10 multiplied by an
integer power of 10.
Fill in the blanks in the table below. Write the decimal form of the number given in scientific
notation. Then give the calculator’s notation for the scientific notation. This is the only time you
should write this calculator notation. Calculator notation is not acceptable in your written work;
use a human language! The last column is for a word name for the number. In a few rows, you
will write the scientific notation yourself.
Scientific
notation
One billion
dollars
Decimal Notation
Word name for the
number
one billion dollars
9
1.0×10 dollars
One year
Calculator
notation
7
3.16×10
seconds
Distance from
earth to moon
Mass of Mars
Nanosecond
Speed of tv
signals
Atomic mass
unit
Light year
8
3.8×10 meters
23
6.24×10
kilograms
-9
1.0×10
seconds
8
3.0×10
meters/second
-27
1.66×10
kilograms
12
6×10 miles
624 sextillion kg
-27
Just say, “1.66×10
kg”!
15
Light year
9.5×10
meters
One billion light
years
Parsec
Megaparsec
Megabyte =
20
2 bytes
Micron
The number of
stars in the
Milky Way
Diameter of a
carbon-12
atom
meters
16
3.1×10
meters
6
10 parsecs
220 = 1,048,576
bytes
bytes
One millionth of a
meter
About one hundred
billion
-14
7.5×10
meters
Rosalie A. Dance and James T. Sandefur, 2004
This material is based upon work supported by the National Science Foundation under Grant No. 0087068.
Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and
do not necessarily reflect the views of the National Science Foundation.
37
Distance from
Earth to Sun
11
1.5×10
meters
Rosalie A. Dance and James T. Sandefur, 2004
This material is based upon work supported by the National Science Foundation under Grant No. 0087068.
Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and
do not necessarily reflect the views of the National Science Foundation.
38
Teaching Guide for
Scientific Notation
The table is intended for fun as well as for gaining awareness and understanding of both
scientific notation and large and small numbers. It is not necessary for any student to do all of
it. This might be an opportunity for students to share results rather than engage in getting all
results together as usual. Of course, each student should be sure (s)he understands all the
numbers.
Scientific
notation
One billion
dollars
One year
Calculator
-ese for
sci. notat.
Word name for the
number
1E9
one billion dollars
31,600,000 seconds
3.16E7
380,000,000 meters
3.8E8
6.24E23
Thirty one million six
hundred thousand
sec.
Three hundred eighty
million meters
624 sextillion kg
0.000000001 second
1E-9
1 billionth of a second
300,000,000 m/sec
3E8
Three hundred million
meters per second
-27
Just say, “1.66×10
kg”!
Six trillion miles
Nine quadrillion five
hundred trillion meters
Nine septillion five
hundred sextillion m.
Thirtyone quadrillion
m
One million parsecs
One million,forty eight
thousand, five
hundred seventy six
One millionth of a
meter
About one hundred
billion
Decimal Notation
$1,000,000,000
9
1.0×10 dollars
7
3.16×10
seconds
Distance from
earth to moon
Mass of Mars
8
Megaparsec
Megabyte =
20
2 bytes
3.8×10 meters
23
6.24×10
kilograms
-9
1.0×10
seconds
8
3.0×10
meters/second
-27
1.66×10
kilograms
12
6×10 miles
15
9.5×10
meters
24
9.5×10
meters
16
3.1×10
meters
6
10 parsecs
6
≈ 1.05 ×10
bytes
Micron
10 meters
The number of
stars in the
Milky Way
Diameter of a
carbon-12
atom
Distance from
Earth to Sun
10 stars
Nanosecond
Speed of tv
signals
Atomic mass
unit
Light year
Light year
One billion light
years
Parsec
624,000,000,000,000,000,000,000 kg
0.00000000000000000000000000166
1.66E-27
kg
6,000,000,000,000 mi.
9,500,000,000,000,000 m
6E12
9.5E15
9,500,000,000,000,000,000,000,000 m
9.5E24
31,000,000,000,000,000 m
3.1E16
1,000,000 parsecs
1E6
1.05E6
20
2
= 1,048,576 bytes
-6
0.000001 m
1E-6
11
100,000,000,000,000
stars
1E11
-14
0.000000000000075 m
7.5E-14
11
150,000,000,000 m
1.5E11
7.5×10
meters
1.5×10
meters
Seventy five
quadrillionths of a
meter
One hundred fifty
billion meters
Rosalie A. Dance and James T. Sandefur, 2004
This material is based upon work supported by the National Science Foundation under Grant No. 0087068.
Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and
do not necessarily reflect the views of the National Science Foundation.
39
Rosalie A. Dance and James T. Sandefur, 2004
This material is based upon work supported by the National Science Foundation under Grant No. 0087068.
Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and
do not necessarily reflect the views of the National Science Foundation.