Unit 2 Vocabulary 3º ESO
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Transcript of Unit 2 Vocabulary 3º ESO
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8/3/2019 Unit 2 Vocabulary 3 ESO
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UNIT 2: Powers and roots.
Rounding numbers.
1.Powers-Powers of positive exponent. To raise a fraction to a power both the numerator and
the denominator rises up to the exponent.
y Example: a1 = a an = aaa (n of times)
Properties
1. a4a3 = (aaaa)(aaa) = a432. (a4)3 = a43 = a123. (ab)3 = a3b34. [a/b]3 = a/ba/ba/b=a3/b35. a4/a3 = a4-3
For example: 81
= 8, (-6)4
= (-6)(-6)(-6)(-6), (2/7)3
= 2/72/72/7
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2.Exacts Roots-Square Roots. = 5, because 52 = 25
, because (5/2)2
= (52
/ 22
) =
-Cube Roots. They are similar to the square roots.
= 2, because 23 = 8-Other Roots. Of the same form, we interpret roots of superior index to 3.
25 = 32, = 2
= 10, because 104 = 10000
In general: ifa = bn , so = b
3.RadicalThe expressions in that they appear indicated roots are
denominated radical.
y Some rules for the managing of radical.-Sum. Radicals with the same radicand and the same index:
3 - + 5 = 7The sum of radical of different radicands or different indexes has to
be made indicated, since it is not possible to simplify:
+ y + -Product. Radicals with the same index:
= =
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Radicals with different indexes cant multiply directly:
(It is not possible to multiply if one does nottransform before both radical ones)
-Power. The power of the radical one can be simplified if the exponent of
the power is multiple of the index of the root.
( ) 6 = ( ) 32 = 72 ( ) 5 It isnt possible to simplify.
4.Rational and Irrational Numbers-Rational Numbers. A rational number is any number that can be
expressed as the quotient
of two integers, with the denominator b not equalto zero.
For example:
=
-Irrational Numbers. An irrational number is a number that cannot be written
as a simple fraction.
Example: (pi) is an irrational number. The value of is:
3.1415926535897932384626433832795 (and more)
RationalNumbers
Fractions
Terminating
DecimalsRecurringDecimals
Integers
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5.Approximation and Rounding-When rounding numbers to a given degree of accuracy, look at the next digit. If it
is 5 or more then round up, otherwise round down.
Example: To round 654.394 to 2 decimal places, look at the thousandths digit.
The thousandths digit is 4, so round down to 654.39.
654.394 654.39 (to 2 decimal places)
Numbers can be rounded:
y To decimal places -> 4.16 = 4.2 to 1 decimal placey To the nearest unit, 10, 100, 1000,
32 559 = 33000 to the nearest thousand
The first non-zero digit in a number is called the 1st
significant figure it has the highest
value in the number.
When rounding to significant figures, count from the first non-zero digit.
Examples: 62.89 63 (to 2 significant figures)
0.00205 0.0021 (to 2 significant figures)
4.267 4.27 (to 3 significant figures)
You can estimate the answer to a calculation by rounding the numbers.
Example:
= 1.35
654.394
654.39
654.395
654.40
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6.Standard Index Form.You use standard form to represent large numbers.
A number is written as A10n
-A is a number between 1 and 10
-The value of n is an integer.
For example: 16000= 1,6104
Standard Form For Small Numbers.
It is useful to write small numbers, like 0.0002 in standard form.
Example: 0.000034=3.410-5
M Isabel Rodrguez y Alba Ruiz
I have used yellow to highlight the most relevant mistakes. Could you tell
me why?
Luis Rodrguez.