Scientific notation

1
Scientific notation
a great way for writing really big
numbers. Instead of ...
602,300,000,000,000,000,000,000
move decimal until theres ONE DIGIT to the left
of it
you could write
6.02 x 1023
2
exponent
6.02 x 10
23
base
every number in scientific notation has three
parts
the stem
the base
the exponent
3
its also great for really small numbers, like
0.000 000 000 000 000 000 000 000 000 000 000 034
3.40 x 10-35
the stem
the base
the exponent
4
Significant Digits
7 x 103
7000
7.043 x 103
7043
5
1, 487,328
1.487328 x 106
7 sig. digs
1.48733 x 106
1, 487,328
6 sig. digs
1.4873 x 106
1, 487,328
5 sig. digs
1.487 x 106
1, 487,328
4 sig. digs
1.49 x 106
1, 487,328
3 sig. digs
1.5 x 106
1, 487,328
2 sig. digs
1 x 106
1, 487,328
1 sig. digs
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If you say 1.000 x 103, you actually MEAN
Its 1000, and I can actually measure it down to
the 1s So the real actual measurement is
between 999.5 and 1000.5 (the span is 1) Thats
FOUR sig digs.
If you say 1.0 x 103, you actually MEAN
Its 1000, and I can actually measure it down to
the 100s Somewhere between 9950 and 1050 (the
span is 100) Thats 2 sig digs
If you say 1 x 103, you actually MEAN
Its somewhere between 500 and 1500 (the span is
1000) Thats ONE sig.dig.
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Multiplying...
you can quickly multiply very daunting
numbers for example, with NO CALCULATOR, multiply
the following 137,445,000,000,000,000,000,000 x
342,223,111,000,000,000,000,000
3 x 1046
(1 x 1023) x (3 x 1023)

1. Put in sci notation, 1 sig dig
2. MULTIPLY the bases
3. ADD the exponents
4. Write in proper sci notation

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m meters
nm nanometers one billionth
um micrometers one millionth
mm millimeters one thousandth
km kilometers one thousand
Mm megameters one million
Gm gigameters one billion
add 3 to exponent
mult by 1000 or
add 3 zeros or
add 3 to exponent
mult by 1000 or
add 3 zeros or
examples 6.7 m is ___ um? 6,700,000 or 6.7 x
106 um 42 um is ____ Mm? 42 x 10-12 Mm or 4.2 x
10-11 Mm 77 km ____ mm? 77 x 106 mm 7.7 x
107 mm rem numbers in scientific notation
always have a stem, a base, and an exponent. The
stem always has one digit to the left of the
decimal. the number of digits to the right of
the decimal in the stem depends on the number of
significant digits. in most science
applications, 3 significant digits is sufficient
one digit to the left and 2 digits to the right
of the decimal point. example 2.45 x 1012 or
6.02 x 1023 or 4.00 x 10-14
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SI exponents
MEMORIZE these
nano- micro- milli- (base measurement e.g.
meter) kilo- mega- giga-
billionth millionth thousandth thousand million
billion