Question

answer this question

Answer 1

hiii!!!

here's Ur answer...

1. given :- 3.33333333...

let x be = 3.33333333... ----------(1)

multiplying both sides by 10 since 1 number is repeating.

10 × x = 10 × 3.33333333...

10x = 33.33333333... ----------(2)

subtract equation (1) from equation (2)

10x - x = 33.33333333... - 3.3333333...

9x = 30

x = 30/9

x = 10/3

simplest form of 3.3333333... = 10/3 in the form of p/q

2. given :- 0.181818181818...

let x be = 0.181818181818... ---------(1)

multiplying both sides by 100 since 2 numbers are repeating.

100 × x = 100 × 0.181818181818...

100x = 18.181818181818... ----------(2)

subract equation (1) from equation (2)

100x - x = 18.181818181818... - 0.18181818181818...

99x = 18

x = 18/99

x = 6/33

x = 2/11

simplest form of 0.181818181818... in the form of p/q is 2/11

3. given :- 0.003232323232...

let x be = 0.0032323232... ----------(1)

multiplying both sides by 100 since 2 numbers are repeating.

100 × x = 100 × 0.003232323232...

100x = 0.323232323232... -----------(2)

subtract equation (1) from equation (2)

100x - x = 0.32323232... - 0.0032323232...

99x = 0.32

x = 0.32/99

simplest form of 0.0032323232... in the form of p/q is = 0.32/99

4. given :- 2.317317317317...

let x be = 2.317317317317... -----------(1)

multiplying both sides by 1000 since 3 numbers are repeating.

1000 × x = 1000 × 2.317317317317...

1000x = 2317.317317317... -----------(2)

subtract equation (1) from equation (2)

1000x - x = 2317.317317317... - 2.317317317...

999x = 2315

x = 2315/999

simplest form of 2.317317317... in the form of p/q is 2315/999

5. given :- 15.712121212...

let x be = 15.712121212... -----------(1)

multiplying both sides by 100 since 2 numbers are repeating.

100 × x = 100 × 15.712121212...

100x = 1571.2121212... -----------(2)

subract equation (1) from equation (2)

100x - x = 1571.212121212... - 15.712121212...

99x = 1555.5

x = 1555.5/99

x = 518.5/33

simplest form of 15.713121212... in the form of p/q is 518.5/34

6. given :- 32.1235353535...

let x be = 32.1235353535...

multiplying both sides by 100 since 2 numbers are repeating.

100 × x = 100 × 32.1235353535...

100x = 3212.3535353535... -----------(2)

subract equation (1) from equation (2)

100x - x = 3212.35353535... - 32.1235353535...

99x = 3180.23

x = 3180.23/99

simplest form of 32.1235353535... in the form of p/q is 3180.23/99

hope this helps and sorry for being late :-(