unit 2 vocabulary 3º eso

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.

unit 2 vocabulary 3º eso

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