Finding Terminating and Non-Terminating values
1). 12/100 = 0.12 (Terminating)
2). 24/50 = 0.48 (Terminating)
3). 1/13 = 0.076923… (Non-Terminating and Non-Repeating)
4). 7/15 = 0.4666… (Non-Terminating and Repeating)
5). 28/12 = 2.333… (Non-Terminating and Repeating)
6). 16/10 = 1.6 (Terminating)
7). 18/200 = 0.09 (Terminating)
8). 5/15 = 0.333… (Non-Terminating and Repeating)
9). 7/19 =0.3684… (Non-Terminating and Non-Repeating)
10). 326/400 = 0.815 (Terminating)
11). 126/516 = 0.244186… (Non-Terminating and Non-Repeating)
Note ;-
* The fraction which complete itself on dividing is called
Terminating Ex. 0.12, 0.14
* The fraction which do not complete itself on dividing but
value repeats number is called ‘Non-Terminating and Repeating’Ex. 0.1222…, 0.1444…
* The fraction which do not complete itself on dividing and
also do not repeats number is called ‘Non-Terminating and Non-Repeating’Ex.
0.12342…, 0.15874…
Finding Rational or Irrational numbers
1). √23 = Irrational number (Non-terminating and non-repeating)2). √225 = 15 = Rational numbers (Perfect Square)
3). 0.3796 = Rational number (Terminating)
4). 7.478478... = Irrational number (Non-terminating and repeating)
5). 1.10100 = Irrational number (Non-terminating and non-repeating)
6). 3.143247... = Irrational number (Non-terminating and non-repeating)
7). √625 = 25 = Rational numbers (Perfect Square)
8). √32 = Irrational number (Non-terminating and non-repeating)
9). √11 = Irrational number (Non-terminating and non-repeating)
10). √196 = 14 = Rational numbers (Perfect Square)
11). 2-√5 = Irrational numbers (Non-terminating and non-repeating)
12). (3 - √23) - √23 = 3 = Rational numbers (Integer)
13). 2√7 / 7√7 = 2 / 7 = Rational numbers (In form of P/Q)
14). 1 / √2 = Irrational numbers (Non-terminating and non-repeating)
15). 2 Pie = Irrational numbers (Non-terminating and non-repeating)
16). 2-√3 = Irrational numbers (Non-terminating and non-repeating)
17). (3 - √25) - √25 = 3 Rational numbers (Integer)
18). 1√2 / 3√2 = 1 / 3 Rational numbers (In form of P/Q)
19). 1 / √3 = Irrational numbers (Non-terminating and non-repeating)
20). 3 Pie = Irrational numbers (Non-terminating and non-repeating)
Note -: * Every 'Non-terminating and non-repeating' and 'Non-terminating and repeating' values are always Irrational Number.
* Every Integer and Terminating value is always a Rational Number.
Multipication
1). ( 3 + √3 ) * ( 2 + √2 ) = 6 + 3√2 + 2√3 + √6
2). ( 3 + √3 ) * ( 3 - √3 ) = 3^2 – (√3)^2
= 9 – 3 = 6 {( a^2 – b^2 ) = (a+b)*(a-b)}
3). ( 2 + √3 ) * ( 2 - √3 ) = 2^2 – (√3)^2 = 4 – 3 = 1 {( a^2
– b^2 ) = (a+b)*(a-b)}
4). ( 4 + √7 ) * ( 5 + √5 ) = 20 + 4√5
+ 5√7
+ √35
5). ( 1 + √3 ) * ( 2 + √2 ) = 2 + √2
+ 2√3
+ √6
6). ( √5 + √3 ) * ( √5 - √3 ) = (√5)^2 – (√3)^2
= 5 – 3 = 2 {( a^2 – b^2 ) = (a+b)*(a-b)}
7). ( √5 + √2 ) * ( √5 - √2 ) = (√5)^2 – (√2)^2
= 5 – 2 = 3 {( a^2 – b^2 ) = (a+b)*(a-b)}
8). (√5 + √2) ^ 2 = (√5)^2 + (√2)^2 + 2*√5*√2
= 5 + 2 + 2√10
= 7 + 2√10
{(a + b)^2 = a^2 + b^2 + 2*a*b)}
9). ( √5
+ √3
) ^ 2 = (√5)^2
+ (√3)^2
+ 2*√5*√3 =
5 + 3 + 2√15
= 8 +2√15 {(a + b)^2 = a^2 + b^2 + 2*a*b)}
10). ( √5 - √2 ) ^ 2 = (√5)^2 + (√2)^2 - 2*√5*√2 = 5 + 2 - 2√10 = 7 - 2√10 {(a - b)^2 = a^2 + b^2 - 2*a*b)}
11). ( √5 - √3 ) ^ 2 = (√5)^2 + (√3)^2 - 2*√5*√3 = 5 + 3 + 2√15 = 8 - 2 √15
{(a - b)^2 = a^2 + b^2 - 2*a*b)}
Note ;- Point To remember
*{( a^2 – b^2 ) = (a+b)*(a-b)}
* {(a + b)^2 = a^2 + b^2 + 2*a*b)}
*{(a - b)^2 = a^2 + b^2 - 2*a*b)}
Hi. I’m Designer of Blog Magic. I’m CEO/Founder of ThemeXpose. I’m Creative Art Director, Web Designer, UI/UX Designer, Interaction Designer, Industrial Designer, Web Developer, Business Enthusiast, StartUp Enthusiast, Speaker, Writer and Photographer. Inspired to make things looks better.
0 comments:
Post a Comment