Write the following number in p q form. 0 . 555

Given: 0 . 555 First we change it in the form of fraction and then reduce it to the lowest terms. To convert a decimal to a fraction, place the decimal number over its place value. ⇒ 0 . 555 = 555 1000 Now, converting the above to the standard form of, we get 555 1000 = 111 200 Therefore, p q form of 0 . 555 is 111 200

Write the following number in p q form. 29 . 568

Here we have, 29 . 568 ¯ Let x = 29 . 568 = 29 . 568568 . . . . . - - - - ( i ) Multiplying ( i ) by 1000 , we get 1000 x = 29568 . 568568 . . . . . . . - - - - ( ii ) Subtracting ( ii ) from ( i ) , we get 1000 x - x = 29568 . 568568 – 29 . 568568 ⇒ 999 x = 29539 . 0 ⇒ x = 29539 999 ⇒ 29 . 568 = 29539 999

Write the following number in p q form. 9 . 315 315 . . .

Here we have, 9 . 315315 . . . Let x = 9 . 315315 … - - - - ( i ) Multiplying both sides by 1000 , we get 1000 x = 9315 . 315315 . . . . . . - - - - ( ii ) Now, subtracting ( i ) from ( ii ) , we get 1000 x - x = 9315 . 315315 – 9 . 315315 ⇒ 999 x = 9306 . 0 ⇒ x = 9306 . 0 999

Write the following number in p q form. 357 . 417417

Here we have, 357 . 417417 let x = 357 . 417417 … Multiplying both sides by 1000 , we get ⇒ 1000 x = 357417 . 417417 … Now, subtracting ( i ) from ( ii ) , we get 1000 x - x = 357417 . 417417 – 357 . 417417 ⇒ 999 x = 357060 . 0 ⇒ x = 357060 999 Therefore, 357 . 417417 = 357060 999

Write the following number in p q form. 30 . 219 ¯

Here we have, 30 . 219 ¯ Let x = 30 . 219 = 30 . 219219 . . . . . . - - - - ( i ) Multiplying both sides by 1000 , we get 1000 x = 30219 . 219219 … - - - - ( ii ) Now, subtracting ( i ) from ( ii ) , we get 1000 x - x = 30219 . 219219 – 30 . 219219 ⇒ 999 x = 30189 . 0 ⇒ x = 30189 999 Therefore, 30 . 219 = 30189 999