Download 1.6 Notes Scientific Notation Standard Form → Scientific Notation

1.6 Notes Scientific Notation

A number is expressed in scientific notation, when it is written as the product of a number
between 1 and 10, and a power of 10.
Standard Form → Scientific Notation


Find a decimal point (or add one at the end if there is none).
Move the decimal point along the number to a new position,
Stop when only one non-zero digit left in front of the decimal point.
 The # of moves is recorded as the power of 10 .
 ? Is my number in standard form small or BIG number????
o If it was a decimal less than 1 (small #), the
o If it was a number greater than 10 (BIG #), the
exponent will be NEGATIVE .
exponent will be POSITIVE
Example: 5,700,000 = 5.7 ×
Example: 0.000072 = 7.2 ×
Scientific Notation → Standard Form
Positive exponent: Multiply the number by a
power of 10; OR move the decimal point to the
right as many spaces as the exponent . Fill in the
spaces at the end with zeros . Remember: we
want a BIG number!
Example:
Negative exponent: The result will be less than 1 .
Move the decimal point to the left as many spaces
as the exponent . Fill in the spaces in front with
zeros .
Example:
1.0305 ×
4.309 ×
= 0.0004309
103,050,000
Comparing Numbers in Scientific Notation: DO NOT rewrite them in standard form!
1) FIRST compare the exponents. Greater exponent means greater number.
2) ONLY if the exponents are the same, compare their decimals.
Compare
1. 6.23 ×
and 8.912 ×
2. 5.15 ×
>
or 6.35 ×
3. 3.28 ×
and 4.25 ×
>
<
Order the real numbers from least to greatest
a) 2.81 ×
2.72 ×
; 2.01 ×
; 2.81 ×
; 2.72 ×
; 9.45 ×
; 9.45 ×
.
; 2.01 ×
b) 135%, 13.5,
, 3.9 ×
1.35(1) 13.5(4) 4.555… (3)
Answer: 135%, √
,
, √
390(5)
4.472… (2)
, 13.5, 3.9 ×