Question

1. Express the following numbers in the form of p / q
(a) -25.6875 (b) 0.621621621.. (c) 15.712121212
2. Write one rational & one fractional number between 0.515115111…. and 0.535335333….
3. Write one example each of two irrational numbers whose:
(a) Sum is a rational number
(b) Product is an irrational number
(c) Difference is an irrational number
(d) Quotient is a rational number
4. Simplify: [ { (625) -1/2 } -1/4 ] 2
5. (a) Find the value of x if 2x-7 x 5x-4 =1250
(b) Find the value of x and y if: 3 x-1 = 9 & 4y+2 = 64
6. Find the value of a & b if 5 + 2√3
7+4√3
= a + b√3
7. If x = 3 + √8, then find the value of x2 + 1/ x2

Answer 1

Answer:

Here's your answer

a) -25.6875= -256875/10000

= 51375/200

= 10275/400

= 2055/8

= 411/16

b)0.621621621

->Let us assume x=0.621______(i)

Therefore x=0.621621

Now we will multiply equation (i) on both sides with 1000 as three numbers are repeating.

1000x = 621.621_______(ii)

Now we will subtract both the equations

1000x-x = 621-0

999x = 621

x = 621/999

x = 3/37

c) 15.7121212....

->Let us assume x=15.712_______(i)

Therefore x=15.7121212

Now we will multiply equation (i) on both sides with 10 as one number is not repeating.

10x = 157.12________(ii)

Now we will multiply equation (ii) on both sides with 100 as two numbers are repeating.

100x = 15712.1212_________(iii)

Now we will subtract equation (ii) and (iii)

100x-10x = 15712-157

90x = 15555

x = 15555/90

x = 311/45

Hope this will help you dear friend.