Scientific Notation A method for re- writing really, really big and really, really small numbers as a power of ten.
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Scientific Notation
A method for re-writing really, really big
and really, really small
numbers as a power of ten.
Really BIG numbers and really
small numbers have too many digits to fit
on a calculator.
A number that is written in scientific notation must
have . . .
1) a decimal point after the first non-
zero digit ex) 7.08
2) a number in the tenths position
ex) 2.0
3) be written as a product of a power of
10 ex) 3.45x109
BIG Numbers
1 000 000 000 000 000The decimalpoint of anywhole numberis at the end ofthe number.
To change this number to scientificnotation, the decimalpoint has to move tothe right of the first non-zero number.
BIG Numbers
1 000 000 000 000 000
To get the decimal point to the new position required for scientific notation, the decimal has to travel 15 place values to reach the position immediately to the right of the first non-zero number. That means it has moved 15 multiples of 10 or . . .
1015
BIG Numbers
1 000 000 000 000 000
To get the decimal point to the new position required for scientific notation, the decimal has to travel 15 place values to reach the position immediately to the right of the first non-zero number. That means it has moved 15 multiples of 10 or . . .
1015
BIG Numbers1 000 000 000 000 000
Disappear
1.0 1015
1) the decimal point is after the first non-zero digit
2) a number is in the tenths position3) it is written as a product of a power
of 10
BIG NumbersConvert to scientific notation.
Where is the decimal point in this number?After the last zero.
Where does the decimal point need to move to?Between the 1 and the 2.
How many place values will the decimal point move?11
What is the answer?
1.23 1011
a) 123 000 000 000 =
BIG NumbersConvert to scientific notation.
1.23 1011
1) the decimal point is after the first non-zero digit
2) a number is in the tenths position3) it is written as a product of a power of
10
a) 123 000 000 000 =
BIG NumbersConvert to scientific notation.
Where does the decimal place need to move to?Between the 6 and the 0.
How many place values will the decimal point move?
13What is the answer?
6.051013
a) 60 500 000 000 000=
BIG NumbersConvert to standard form.
c) 4.7 108
The exponent (8) tells you how many place values needs to be put back into the number.
4.70 0 0 0 0 00 = 470 000 000
BIG NumbersConvert to standard form.
The exponent (11) tells you how many place values needs to be put back into the number.
d)9.04 1011
9.0 40 0 0 0 0 00 0 0 = 904 000 000 000
SMALL NumbersConvert to scientific notation.
a)0.0000000012Where does the decimal point need to move to?
Between the 1 and 2.How many place values does the decimal need tomove? (Notice the decimal has to move to the right)
-9
0.0 0 0 0 00 0 012
What is the answer?
1.2 10 9
SMALL NumbersConvert to scientific notation.
a)0.0000000012 1.2 10 9
1) the decimal point is after the first non-zero digit
2) a number is in the tenths position3) it is written as a product of a power of
10
SMALL NumbersConvert to scientific notation.
b)0.00009008Where does the decimal point need to move to?
Between the 9 and the 0.
How many place values does the decimal pointneed to move?
-5
0.0 0 0 09 0 08
What is the answer?
9.00810 5
SMALL NumbersConvert to standard form.
c)8.4110 9
How many place values need to be put back intothe number?
-9
0 0 0 0 00 0 0 08.41
Notice that there is an extra zero for the ones place value.
What is the answer?
0.00000000841
SMALL NumbersConvert to standard form.
How many place values need to be put back intothe number?
-7
d)9.06110 7
0 0 0 0 00 0 9.061
What is the answer?
0.0000009061
Adding Numbers in Scientific Notation
Remember - Whenever you add or subtract in math, “things”must be the same.To add or subtract decimal numbers, place values must bethe same. To insure this one must convert both numbersto standard form first.
2.3105 3.05 105
230,000 305,000
230 000305 000+
Multiplying Numbers in Scientific Notation
Remember - When multiplying powers with the same baseyou can add the exponents.
a) 0.3104 6.3105 Reorder and regroup.
0.3 6.3 104 105 Follow BODMAS.
6.3
0.3
1.89
104 105 1045 109
What is the answer?
1.89 109
Multiplying Numbers in Scientific Notation
Reorder and regroup.
b) 0.32 10 5 1.5102
0.32 1.5 10 5 102 Follow BODMAS
0.32
1.5
160
320
.480
10 5 102 10 52 10 3
What is the answer?
.480 10 3
But wait, is this answer in scientific notation form?
Multiplying Numbers in Scientific Notation
b) 0.32 10 5 1.5102 .480 10 3
Why is this not considered in the correct form?
The decimal point is not after the first non-zero number.
.4 80 10 3
If the decimal point has to move one more place valueto the right, what will happen to the exponent on the power?The exponent has to decrease one to move one place value to the right.
Multiplying Numbers in Scientific Notation
b) 0.32 10 5 1.5102 .4 80 10 3 4.810 4
Dividing Numbers in Scientific Notation
a)2.3 104
4.6 107
Remember - When dividing powers with the same basejust subtract exponents on those like bases.
Separate into two separate fractions.2.34.6
104
107
Divide. 4.6 2.3 46 23.0
0.5 230
104
107 104 7 10 3
Dividing Numbers in Scientific Notation
a)2.3 104
4.6 107
4.6 2.3 46 23.00.5
230
104
107 104 7 10 3
The result is . . . 0.510 3
But this in not in the correct form for scientific notation.What needs to happen? 0.510 3
Decrease the exponentby 1
The answer is . . .
5.0 10 4
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