Introduction to Scientific Notation
Aim: Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large
or very small quantities, and to express how many times as much one is than the other. Perform operations
with numbers expressed in scientific notation. (8.EE.2 and 8.EE.3)
Scientific Notation
Scientific Notation is a shorthand way of expressing a very large or very small number as
the product of a factor and an integer power of 10. The factor must be greater than or
equal to 1 and less than 10.
a x 10n
where 1 ≤ a < 10 and n is an integer
To express a number in scientific notation:
 If the number is greater than or equal to 1, the power of ten is positive.
This represents a very large number.
 If the number is between 0 and 1, the power of ten is negative.
This represents a very small number.
Examples:
Standard Form
Scientific Notation
This Number Is:
89,000,000
8.9 X 107
Very Large
0.00000432
4.32 X 10-6
Very Small
Discuss:
Why is scientific notation useful in the real world?
Practice Exercises:
Is the number below in scientific notation? Write YES or NO.
1.
3.2 X 103 __________________
2.
62.1 X 10-9__________________
3.
0.87 X 102__________________
4.
6.9 X 10-8 ___________________
5.
5 X 10-5__________________
6.
0.763 X 10-8__________________
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Converting Numbers from Standard Form to Scientific Notation
Exercise 7:
Jupiter’s minimum distance from the sun is about 460,000,000 miles.
This number is written in ________________
_________________.
Step 1: The number must be written as greater than or equal to 1
but less than 10.
Step 2: Determine the exponent for the power of 10.
Count the number of places that the decimal point was moved.
The decimal was moved ______ places to the left. Since the
original number is greater than 1, the exponent is
To convert this number into
scientific notation:
460,000,000 = 4.6 x 10?
END
START
4.6 0 0 0 0 0 0 0
decimal moved left 8 places
_______________.
Write the number in scientific notation: __________________.
Exercise 8:
Mr. Kendall measured a specimen that was 0.00000045 of a millimeter long.
This number is written in ___________ ___________
Step 1: The number must be written as greater
than or equal to 1, but less than 10.
Step 2: Determine the exponent for the power of 10.
Count the number of places that the decimal point was moved.
To convert this number into
scientific notation:
0.00000045 = 4.5 x 10?
The decimal was moved ______ places to the right. Since the
original number is less than 1, the exponent is
START
END
0. 0 0 0 0 0 0 4 5
_______________.
decimal moved right 7 places
Write the number in scientific notation: _____________________.
Practice Exercises:
9. In 2010, the population of the United States was about 309,000,000. Write this number in
scientific notation.
10. The cornea of the eye is 0.00056 meter thick. Write this number in scientific
notation.
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Converting Numbers from Scientific Notation to Standard Form
Exercise 11:
The average distance from the Earth to the moon is approximately 3.8 x 108 meters.
This number is written in __________________________.
To convert this number into standard form:
 This number is a very ___________ number.
3.8 x 108 = 3 8 0 0 0 0 0 0 0
 To rewrite this number in standard form,
the decimal point needs to moved to the
decimal moves right 8 places
= 380,000,000
___________, __________ times.
 Then you will need to fill in the blank spaces with __________.
 Write this number in standard form:
3.8 x 108 = _________________
Exercise 12:
The width of a thin wire is 6.7 x 10-4 m.
This number is written in ______________________
To convert this number into standard form:

This number is a very ___________ number.

To rewrite this number in standard form,
6.7 x 10−4 = 0 0 0 0 6 7
the decimal point needs to moved to the
___________, __________ times.
decimal moves left 4 places
= 0.00067

Then you will need to fill in the blank spaces with _______.

Write this number in standard form: 6.7 x 10−4 = ___________________
Practice Exercises:
13. An acre is about 4.05 x 107 square centimeters. Write this number in standard form.
14. The diameter of a human hair is about 9.9 x 10-5 meter. Write this number in
standard form.
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Name __________________________ Period ____
Introduction to Scientific Notation Homework
Date __________
For #1 – 4, if the number is in scientific notation, write correct. If it’s not, state
the reason why, and rewrite it in scientific notation.
1.
6.404 x 104 __________________________________________
2.
0.98 x 10-7___________________________________________
3.
39.0 x 102 ___________________________________________
4.
8.49 x 10-4___________________________________________
For #5 - 8, write the following numbers in scientific notation.
5. 0.0000495
6. 549,000,000
7.
700,000,000,000
8.
0.00000005
For # 9 - 12, write the following numbers in standard form.
9. 4.5 x 106
10. 9.405 x 10-8
11.
7.3 x 10-10
12.
6.777 x 107
Answer each question below:
13. In 2000, the top attendance at an amusement park in the United States was
15,400,000 people. Write the number of people in scientific notation.
14.
The planet Mercury is an estimated 3.598  107 miles from the Sun. Write the
distance Mercury is from the Sun in Standard form.
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