Scientific Notation is simply a method for expressing and working with very large or
very small numbers. It is a short hand method for writing numbers. Numbers in
scientific notation are made up for three parts: the
coefficient, the base and the exponent. Observe the
example on the right. This is the scientific notation for the
standard number 21 600 000.
Scientific Notation is simply a method for expressing and working with very large or
very small numbers. It is a short hand method for writing numbers. Numbers in
scientific notation are made up for three parts: the
coefficient, the base and the exponent. Observe the
example on the right. This is the scientific notation for the
standard number 21 600 000.
In order for a number to be in correct scientific notation, the following conditions
must be true:
1. The coefficient must be greater than or equal to one and less than 10.
In other words, there must be one and only one (nonzero) digit to the
left of the decimal point.
2. The base must be 10.
3. The exponent must show the number of decimal places that the
decimal needs to be moved to change the number to standard notation.
In order for a number to be in correct scientific notation, the following conditions
must be true:
4. The coefficient must be greater than or equal to one and less than 10.
In other words, there must be one and only one (nonzero) digit to the
left of the decimal point.
5. The base must be 10.
6. The exponent must show the number of decimal places that the
decimal needs to be moved to change the number to standard notation.
Changing numbers from Standard (decimal) Notation to Scientific Notation:
 Change 536 200 000 000 into scientific notation.
Changing numbers from Standard (decimal) Notation to Scientific Notation:
 Change 536 200 000 000 into scientific notation.
The decimal point must move to behind the 5 to make the coefficient
have only one digit to the left of the decimal point. That will make the
coefficient be 5.362. The decimal point moved 11 palces to the left,
making the exponent 11. Therefore, 536 200 000 000 = 5.362 x 1011.
The decimal point must move to behind the 5 to make the coefficient
have only one digit to the left of the decimal point. That will make the
coefficient be 5.362. The decimal point moved 11 palces to the left,
making the exponent 11. Therefore, 536 200 000 000 = 5.362 x 1011.
Here’s another way of looking at it. The original number is very large,
and it’s being changed into a relatively small number (5.362). To make
sure the number has the same value in decimal notation and scientific
notation, you would have to multiply the smaller coefficient by a larger
number, hence the positive power of ten.
Here’s another way of looking at it. The original number is very large,
and it’s being changed into a relatively small number (5.362). To make
sure the number has the same value in decimal notation and scientific
notation, you would have to multiply the smaller coefficient by a larger
number, hence the positive power of ten.
 Change 0.000 000 032 8 into scientific notation.
 Change 0.000 000 032 8 into scientific notation.
The decimal point must move behind the 3 to satisfy condition #1. This
will make the coefficient 3.28. The decimal moves 8 places to the right,
making the exponent -8. Therefore, 0.000 000 032 8 = 3.28 x 10-8.
The decimal point must move behind the 3 to satisfy condition #1. This
will make the coefficient 3.28. The decimal moves 8 places to the right,
making the exponent -8. Therefore, 0.000 000 032 8 = 3.28 x 10-8.
In this case, the original number is very small, and it’s being changed
into a relatively larger number (3.28). To make sure the number has the
same value in decimal notation and scientific notation, you would have
to multiple the larger coefficient by a small number, hence the negative
power of ten.
In this case, the original number is very small, and it’s being changed
into a relatively larger number (3.28). To make sure the number has the
same value in decimal notation and scientific notation, you would have
to multiple the larger coefficient by a small number, hence the negative
power of ten.
Scientific Notation
Practice
Name: _____________________________
Period: _________ Date: _______________
Complete the chart:
Name: _____________________________
Period: _________ Date: _______________
Complete the chart:
Standard Notation
Speed of light in a
vacuum
Half-life of Uranium235
Melting point of
Tungsten
Temperature at which
atomic fusion occurs
Lowest Possible
Temperature
Radius of hydrogen
energy level
Scientific Notation
Practice
Scientific Notation
299293000 m/s
710000000 years
3410 C
1.5 x 107 C
-2.73 x 102 C
5.3 x 10-11 m
Perform the following operations, expressing the answer with the correct
number of significant figures.
1. 1.35 m + 2.467 m ____________
Standard Notation
Speed of light in a
vacuum
Half-life of Uranium235
Melting point of
Tungsten
Temperature at which
atomic fusion occurs
Lowest Possible
Temperature
Radius of hydrogen
energy level
Scientific Notation
299293000 m/s
710000000 years
3410 C
1.5 x 107 C
-2.73 x 102 C
5.3 x 10-11 m
Perform the following operations, expressing the answer with the correct
number of significant figures.
1. 1.35 m + 2.467 m ____________
2. 1 035 m2 ÷ 42 m ____________
2. 1 035 m2 ÷ 42 m ____________
3. 12.01 mL + 35.2 mL + 6 mL ____________
3. 12.01 mL + 35.2 mL + 6 mL ____________
4. 55.46 g – 28.9 g ____________
4. 55.46 g – 28.9 g ____________
5. 0.021 cm  3.2 cm  100.1 cm ____________
5. 0.021 cm  3.2 cm  100.1 cm ____________
6. 0.15 cm + 1.15 cm + 2.051 cm ____________
6. 0.15 cm + 1.15 cm + 2.051 cm ____________
7. 150 cm3 ÷ 4 cm ____________
7. 150 cm3 ÷ 4 cm ____________
8. 505 kg - 450.25 kg ____________
8. 505 kg - 450.25 kg ____________
9. 1.252 mm  0.115 mm  0.012 mm ___________
9. 1.252 mm  0.115 mm  0.012 mm ___________
10. 1.278 x 103 m2 ÷ 1.4267 x 102 m ____________
10. 1.278 x 103 m2 ÷ 1.4267 x 102 m ____________
11. 5.29 x 104 m  4.43 x 109 m ____________
11. 5.29 x 104 m  4.43 x 109 m ____________
12. 3.00 x 10-6 mm  5.21 x 1013 mm ____________
12. 3.00 x 10-6 mm  5.21 x 1013 mm ____________