Transcript Scientific Notation

Drill – 9/10/10
1.
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3.
4.
5.
66.3 + 101.56 + 0.439 =
56 × 101.45 =
100 ÷ 4.56 =
67.0 – 0.235 =
2114 ÷ 21 =
Scientific Notation
What do you think about these numbers?
Number of atoms in 1g of Hydrogen =
602200000000000000000000
Size of a hydrogen atom =
0.000000000053 meters
Mass on an electron =
0.00000000000000000000000000000009109382
kilograms
• Scientists use very large and very small
numbers frequently. It is difficult to write,
read, and keep track of all those zeros.
Fortunately, scientists devised a way to
write large or small numbers in an easier
way.
How to change a number to scientific notation
1. Move the decimal point so that only one digit (1-9,
not zero) is to the left of the decimal
2. Write that number with only its significant figures
3. Write “×10”
4. Put an exponent on the 10 that reflects how many
places you moved the decimal.
5. Include a negative sign if necessary. If you need to
multiply by 10’s to get back to your original number,
it is a positive exponent (no sign). If you need to
divide by 10’s to get back to the original number, it
is a negative exponent (add a negative sign in front
of the exponent)
Write in Scientific Notation
1. 100000
2. 100000.00
3. 0.000456
4. 0.0200
How to change a number out of
scientific notation
1. Look at the exponent.
If it is positive then the number will get
bigger. That means the decimal will be
moved that many places to the right.
If it is negative then the number will get
smaller. That means the decimal will be
moved that many places to the left.
Write in Standard Notation
8
6.96×10 m
1.
-4
2. 1.0×10 mL
• Anytime your exponent gets bigger, the
number in front gets smaller.
• Anytime the exponent gets smaller, the
number in front gets bigger.
Math in Scientific Notation
Multiplication and Division with Scientific Notation
For multiplication, you simply multiply
the leading numbers and add the
powers of ten.
2×109 multiplied by 3×104 would just be
(2×3)×109+4 = 6×1013.
Similarly, for division you divide the
leading numbers and subtract the
powers of ten.
6×105 divided by 2.2×101 would be
(6÷2.2)×105-1 = 3×104.
Things to remember:
• Don’t forget your Sig Fig rules – they apply
here!
Ex: (4.0×103)(1.034×106) = 4.1×109
• Make sure your answer is in correct
scientific notation with only 1 digit (1-9) to
the left of the decimal!
Ex: (5.2×1011)(4.00×108) = 2.1×1020
Addition & Subtraction with Scientific
Notation
• Addition or subtraction can only occur if
the numbers have the same exponent.
Once the exponents are equal then you
can add or subtract as usual and carry
down the exponent.
• Ex: 4.2 x 104 kg + 0.79 x 104 kg
= 4.99 x 104 rounded to 5.0 x 104 kg
3
Ex: 5.0 x 10 mL +
4
6.5 x 10 mL
We need to either change:
5.0 x 103 mL to 0.50 x 104 mL
OR
6.5 x 104 mL to 65 x 103 mL
5.0 x 103 mL
.50 x 104 mL
+ 65 x 103 mL
+ 6.5 x 104 mL
70. x 103 mL = 7.0 x 104 mL
7.0 x 104 mL
Ex: 2.001 x 1012 g + 1.550 x 109 g
1.550 x 109 g = 0.001550 x 1012 g
(the exponent ↑ so the number ↓)
0.001550 x 1012g + 2.001 x 1012g =
2.00255 x 1012g = 2.003 x 1012g
Scientific Notation on the Calculator
• Get out your calculator.
• Find the exponent key (EXP or EE or ?).
This key represents “x 10^” so when you
type hit “4” “EE” “10”, you just typed 4x1010
5.253x104
*
2.34x1052
57
1.23x10
=
2.4012x1013 * 1.343x1033 = 3.225x1046