Scientific notation
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common text message
abbreviation:
“Hey Stacy! Are we still going to
study after school tomorrow?
Well, talk to you later. See you!”
 When
we use abbreviations such as lol, ttyl, idk,
2morro, or cu, we are saving ourselves time and
energy. The purpose it to convert long words or
phrases into short, single strand phrases.
Scientific notation is the same way.
 Notes:
Scientific notation is a
method of expressing very large
or very small numbers in a
concise manner.
Example:
You can write 1,000,000,000,000
But wouldn’t it be easier to write 1.0x1012?
How to convert to S.N.
1) Move the decimal so that it is directly
behind the first non-zero SINGLE digit.
For example:
2,498,0000 -> 2.4980000
2) Drop all of the TRAILING zeroes.
2.4980000 -> 2.498
3) Write x10x behind the newly formed
number, where x (the little one) is the
number of times the decimal was moved.
2,498,0000 ->2.4980000
The decimal was moved 6 times, so we
write,
2.4980000 -> 2.498 -> 2.498x106
General Rules:
 When
we move the decimal to the left,
the exponent is positive. The original
number was greater than one.
 When we move the decimal to the right,
the exponent is negative. The original
number was less than one.
Examples:
240,000,000 -> 2.4x108
0.000049 -> 4.9x10-5
Moving to the left
568 200
1. Move the decimal:
2.
Drop the extra zeroes:
3.
Find the exponent on the 10 (it is best
to do this while moving the decimal):
4.
Finally, write the number in Scientific
Notation (abbreviated S.N.):
Moving to the right
0.000002340000
1. Move the decimal:
2.
Drop the extra zeroes:
3.
Find the exponent on the 10 (remember,
left = positive while right = negative):
4.
Write the number in S.N.:
Questions:
Convert the following standard form numbers
to S.N.:
0.000002500700 244
129 000 000
0.0000000019
4,040
248,945,478
0.250700
782,541
40
0.000008825
1
5,200
0.000505
0.000000000008
56,000
1,782,941
Significant Digits – Scientific Notation
In scientific notation, all numbers prior to
the x are significant.
4.0 × 103 = two sig. digs.
6.724 × 10-18 = four sig. digs.
Converting back to standard form
Option 1:
Multiply the two terms (the decimal
between 1 and 10 and the power of 10).
Ex. 2.14 x 104
= 2.14 x 10000
= 21 400
*This method works because writing
2.14x104 is the same as writing 2.14 x 10 x
10 x 10 x 10*
Option 2:
Move the decimal to the right (if the
exponent is positive) or to the left (if the
exponent is negative) x times, where x is
the value of the exponent (if the exponent
is 4, move the decimal to the right 4
places). Add zeroes where necessary.
Ex. 2.14 x 104
21400.
Questions:
Convert the following S.N. numbers to
standard form:
2.187 x 104
7.9 x 10-9
4.9 x 10-10
3.88 x 10-7
1.001 x104
2.701 x 105
4.7 x 101
1.0 x 10-5
9.472 x 108
4.808 x 10-4
2.80 x 10 11 1.0 x 1012
7.29017 x 108 7.4051 x 10-11 1.0 x 10-12
1.0 x 10-1
2.8 x 105
4.8249 x 104
Comparing values
Identify
the number with the
greater value in the following
pairs:
 2.14
x 102 and 3.14 x 102
 1.0 x 104 and 1.0 x 102
 7.8 x 10-5 and 9.2 x 10-5
 2.2 x 10-2 and 2.2 x 10-4
Metric Unit Conversions
When going from a BIG unit to a smaller
unit (left to right on the chart),
MULTIPLY.
When going from a SMALL unit to a bigger
unit (right to left), DIVIDE.
Each successive movement to the
right/left is a shift of one power of ten.
For example, converting from cm to m
involves TWO moves to the left, so we
DIVIDE by 100 (10x10).
Example
Convert 52 000 centimetres to
kilometres.
Example
Convert 0.00245 g into mg.
Questions:
Answer the following questions to the best
of your ability:
1426 m into km
289 477 g into kg
0.000098 km into cm
24 685 mL into L
0.19 km into mm
0.001 g into mg
2450 mg into g
0.000051 km into mm