What Is Scientific Notation?
By Cindy Grigg
We use numbers to measure many things.
Ordinary numbers are used to measure the
ordinary things we see every day. Ordinary
numbers are called standard notation. When we
need to measure something that is very, very
large or very, very small, then we can use a
system called scientific notation.
1
Scientific notation uses ordinary numbers,
but it expresses them using exponents (or
powers) of the number ten. Scientists who use
large numbers and small numbers can use
scientific notation to shorten the numbers they have to write.
2
What kinds of numbers are written using scientific notation? Distances in space are
often very large numbers. Atoms are very small. When scientists write the weight of
atomic particles, they use scientific notation.
3
A number written in scientific notation is written as the product of a number between
one and ten and a power of ten. Here's an example. You could write a distance of 2,000
miles as 2.0 X 10 3 miles. It is read as "two times ten to the third power." Ten to the third
power (103) means 10 X 10 X 10. When you multiply a number by ten with any
exponent, you move the decimal point to the right. Ten to the third power means that
you move the decimal point three places to the right.
4
Small numbers are written with negative exponents. A negative exponent tells you
that the decimal point is moved that number of places to the left. For example, five cents
is written as $0.05. You could write it in scientific notation as 5.0 X 10-2 dollars.
5
Any number with the exponent of 1 (any number raised to the power of 1) is the
number itself. 21 = 2. 51 = 5. Can the number 1 be written in scientific notation? Yes! Ten
to the zero power (100) = 1. The number 7 would be written as 7 X 100 in scientific
notation.
6
You can see from that example that scientific notation is not so useful for writing
ordinary numbers. But for very large ones or very small ones, it helps avoid having to
write so many zeroes.
7
For example, the mass of the sun is close to
2,000,000,000,000,000,000,000,000,000,000 kg. In scientific notation, it would be
written as 2.0 X 1030 kilograms. See how much simpler that is? The exponent 30 shows
that the decimal point is really 30 places to the right of where it is written in the first
number. The actual mass of the sun is 1,989,000,000,000,000,000,000,000,000,000 kg.
So in scientific notation, it would be written as 1.989 X 1030 kilograms. Then the decimal
point would move thirty places to the right, but three of those places would be 989
followed by twenty-seven zeroes.
8
Remember that small numbers are written with negative exponents. A negative
exponent tells you that the decimal point is moved that number of places to the left. The
diameter of a virus might be 0.000000000011 meters. In scientific notation, it would be
written as 1.1 X 10-11 m. Just remember that the first number that will be multiplied by a
power of ten must be between one and ten.
9
Scientific notation is a simpler and shorter way to write really large or really small
numbers. You just have to know the secret! Numbers with positive exponents will be
large and the zeroes will be added to the right. Numbers with negative exponents will be
small. The zeroes will be added to the left of the first number.
10
Copyright © 2015 edHelper
Date ___________________
Name _____________________________
What Is Scientific Notation?
1. What number is most likely to be
written in scientific notation?
Your weight
The distance from the sun to
Saturn
The distance from your house to
your school
Your bicycle's speed
2. What is 4.0 X 105 written in standard
notation?
4,000
4,000,000
400,000
40,000
3. A number written in scientific notation
with a negative exponent will be
______.
A large number
A small number
A negative number
None of the above
4. What is the correct way to write 8
million (8,000,000) in scientific
notation?
8000 X 103
80.0 X 105
.08 X 106
8.0 X 106
5. What number is written as 100?
0
10
1
None of the above
6. What number is 5-1?
5
-5
0.5
-1
7. Write 0.001 in scientific notation.
8. What number is 5 X 10 -5 written in
standard notation?
-50
50,000
-500,000
0.00005
9. The distance from the Earth to the sun
is about ninety three million miles.
Write that number using scientific
notation.
10. In a year, kids in the U.S. watch
nearly 1,325 hours of TV. Write the
hours of TV-watching in scientific
notation.
What Is Scientific Notation?
By Cindy Grigg
secret
distance
zeroes
zero
shorten
point
moved
distances
multiply
move
writing
positive
itself
standard
written
meters
virus
write
multiplied
system
atomic
Directions: Fill in each blank with the word that best completes the reading comprehension.
We use numbers to measure many things.
Ordinary numbers are used to measure the ordinary
things we see every day. Ordinary numbers are called
(1) _______________________ notation. When we
need to measure something that is very, very large or
very, very small, then we can use a
(2) _______________________ called scientific
notation.
Scientific notation uses ordinary numbers, but it
expresses them using exponents (or powers) of the
number ten. Scientists who use large numbers and
small numbers can use scientific notation to (3) _______________________ the numbers they
have to write.
What kinds of numbers are (4) _______________________ using scientific notation?
(5) _______________________ in space are often very large numbers. Atoms are very small.
When scientists write the weight of (6) _______________________ particles, they use
scientific notation.
A number written in scientific notation is written as the product of a number between one and
ten and a power of ten. Here's an example. You could write a (7) _______________________
of 2,000 miles as 2.0 X 10 3 miles. It is read as "two times ten to the third power." Ten to the
third power (103) means 10 X 10 X 10. When you (8) _______________________ a number
by ten with any exponent, you move the decimal (9) _______________________ to the right.
Ten to the third power means that you move the decimal point three places to the right.
Small numbers are written with negative exponents. A negative exponent tells you that the
decimal point is moved that number of places to the left. For example, five cents is written as
$0.05. You could (10) _______________________ it in scientific notation as 5.0 X 10-2
dollars.
Any number with the exponent of 1 (any number raised to the power of 1) is the number
(11) _______________________ . 21 = 2. 51 = 5. Can the number 1 be written in scientific
notation? Yes! Ten to the (12) _______________________ power (100) = 1. The number 7
would be written as 7 X 100 in scientific notation.
You can see from that example that scientific notation is not so useful for
(13) _______________________ ordinary numbers. But for very large ones or very small
ones, it helps avoid having to write so many zeroes.
For example, the mass of the sun is close to 2,000,000,000,000,000,000,000,000,000,000 kg.
In scientific notation, it would be written as 2.0 X 1030 kilograms. See how much simpler that is?
The exponent 30 shows that the decimal point is really 30 places to the right of where it is
written in the first number. The actual mass of the sun is
1,989,000,000,000,000,000,000,000,000,000 kg. So in scientific notation, it would be written as
1.989 X 1030 kilograms. Then the decimal point would (14) _______________________ thirty
places to the right, but three of those places would be 989 followed by twenty-seven zeroes.
Remember that small numbers are written with negative exponents. A negative exponent tells
you that the decimal point is (15) _______________________ that number of places to the left.
The diameter of a (16) _______________________ might be 0.000000000011
(17) _______________________ . In scientific notation, it would be written as 1.1 X 10-11 m.
Just remember that the first number that will be (18) _______________________ by a power
of ten must be between one and ten.
Scientific notation is a simpler and shorter way to write really large or really small numbers.
You just have to know the (19) _______________________ ! Numbers with
(20) _______________________ exponents will be large and the
(21) _______________________ will be added to the right. Numbers with negative exponents
will be small. The zeroes will be added to the left of the first number.
Name _____________________________
Date ___________________
(Key 1 - Answer ID # 0828300)
Crack the code! Write the real word that each of the codes represent. Each letter in the real
word has been changed to another letter. For example, a B in the code might really mean
C. Once you figure out the code for one letter, the same code is used for all the words on
this sheet.
Code: A B D E F G H I J K L P R T U W Z
S
P
A
Letter:
1.
AFIJDZU
2.
TEJWR
3.
WERZRJEW
4.
HRZWAZGA
5.
ZIRBZU
6.
ZPEJA
7.
HLHRFD
8.
KFGE
9.
PJGBH
10.
DFZWH