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... a way to express very
small or very large numbers
A number written in Scientific Notation
has three parts…
A number
greater
than one
but less
than ten
2.110
A multiplication
sign
3
A power of
ten
Standard Form to Scientific Notation:
(1) Move the decimal point so that the number is
greater than one but less ten .
(2) Remove any insignificant zeros.
(3) Count number of decimal places the decimal
has "moved" from the original number. This
will be the exponent of the 10.
(3) If the original number was a small number, the
exponent is negative; if the original number was
a big number, the exponent is positive.
Try the following Problems:
61,500 = 6.15 10
4
84,960,000 = 8.496  10
321 =
3.21 10
2
7
0.000527 = 5.27  10
0.0000004 = 4  10
4
7
0.004503 = 4.503 10
3
REMEMBER: the first number must be
greater than 1,but less than 10.
Therefore, the number before the decimal
point can be 1, 2, 3, 4, 5, 6, 7, 8, or 9.
Scientific Notation
to
Standard Form:
Scientific Notation to Standard Form:
(1)Move the decimal point the same
number of spaces as the exponent.
(2)Positive exponents = big numbers, so
move the decimal point to the RIGHT.
(3)Negative Exponents = small numbers
so move the decimal point to LEFT
(4)Fill in any empty spaces with zeros and
rewrite the number.
Try the following problems
1.09  10 
5
109,000
4.2273  10  42,273
4
3
9.42  10 
0.00942
Comparing Numbers in
Scientific Notation:
Comparing Numbers in
Scientific Notation:
(1)First compare the powers of ten.
(2)Then compare the decimal values.
Try the following problems
Refer to the table at the right. Order the countries according to
the amount of money visitors spent in the United States from
greatest to least.
United Kingdom, Canada, Mexico, India.
Tell whether the following number is correctly written in Scientific Notation.
Explain how you know.
4
16.2  10
No, because 16.2 is not a number between one and ten. It should be
1.62 x 105
Multiplying Numbers in
Scientific Notation:
Multiplying Numbers in Scientific Notation:
(1)We use the Commutative and Associative
properties.
(2)Multiply the decimals.
(3)Then multiply the powers of 10 by adding
exponents.
(4)Write in scientific notation.
Try the following Problems:
Evaluate (7.2 x 103)(1.6 x 104)
1.152 x 108
Evaluate (8.4 x 102)(2.5 x 106)
2.1 x 109
Evaluate (2.6 x 104)(1.2 x 10-3)
3.1 x 10
The volume of a drop of oil is 0.00002 liter. Find and write the
volume of 8 drops of the oil in scientific notation.
1.6 x 10-4
Dividing Numbers in
Scientific Notation:
Dividing Numbers in Scientific Notation:
(1)We use the Commutative and Associative
properties.
(2)Divide the decimals.
(3)Then divide the powers of 10 by
subtracting exponents.
(4)Write in scientific notation.
Try the following Problems:
Evaluate
Evaluate
Evaluate
6.3 x 104
2.375 x 1011
3.75 x 10-19
Central Park in NYC is rectangular in shape and measures about 1.37 x 104
feet by 2.64 x 102 feet. If one acre is equal to 4.356 x 104 square feet, how
many acres does Central Park cover? Round to the nearest hundredth.
83.03 acres
Adding Numbers in
Scientific Notation:
Adding Numbers in Scientific Notation:
(1)The numbers need to be expressed in the
same form.
(2)This means to rewrite with the same
exponents.
(3)Then factor the GCF (powers of 10).
(4)Line up the decimals to add.
(5)Write in scientific notation.
Try the following Problems:
Evaluate (6.89 x 104) + (9.24 x 105)
9.929 x 105
Evaluate 593,000 + (2.5 x 106)
3.093 x 106
Evaluate (8.9 x 109) + (4.2 x 106)
8.9042 x 109
The length of a rectangle is1.656 x 10-3. The width of the rectangle is 5.52 x 10-4.
Find the perimeter of the rectangle in scientific notation.
4.356 x 10-3
Subtracting Numbers in
Scientific Notation:
Subtracting Numbers in Scientific Notation:
(1)The numbers need to be expressed in the
same form.
(2)This means to rewrite with the same
exponents.
(3)Then factor the GCF (powers of 10).
(4)Line up the decimals to subtract.
(5)Write in scientific notation.
Try the following Problems:
Evaluate (7.83 x 108) - 11,610,000
7.7139 x 108
Evaluate (9.64 x 108) - (5.29 x 106)
9.5871 x 108
Evaluate (1.35 x 106) – 117,000
1.233 x 106
The Earth is 92,957,100 miles from the Sun and Mercury is 35,983,610 miles from the
Sun. About how much further is Earth from Mercury?
5.697349 x 107