i. 0.555
ii. Let x = …(i)
x = 29.568568…
Since, three numbers i.e. 5, 6 and 8 are repeating after the decimal point.
Thus, multiplying both sides by 1000,
1000x = 29568.568568…
1000 x = 29568. bar 568 …(ii)
Subtracting (i) from (ii),
1000x – x = 29568. bar 568 – 29. bar 568
∴ 999x = 29539
iii. Let x = 9.315315 … = 9. bar 315 …(i)
Since, three numbers i.e. 3, 1 and 5 are repeating after the decimal point.
Thus, multiplying both sides by 1000,
1000x = 9315.315315…
∴1000x = 9315. bar 315 …(ii)
Subtracting (i) from (ii),
1000x – x = 9315. bar 315 - 9. bar 315
∴ 999x = 9306
iv. Let x = 357.417417…
= 357. bar 417…(i)
Since, three numbers i.e. 4, 1 and 7 are repeating after the decimal point.
Thus, multiplying both sides by 1000,
1000x = 357417.417417…
∴ 1000x = 357417.417 …(ii)
Subtracting (i) from (ii),
1000x – x = 357417. bar 417 – 357. bar 417
∴ 999x = 357060
v. Let x = 30. bar 219 …(i)
∴ x = 30.219219
Since, three numbers i.e. 2, 1 and 9 are repeating after the decimal point.
Thus, multiplying both sides by 1000,
1000x= 30219.219219…
∴ 1000x = 30219. bar 219 …(ii)
Subtracting (i) from (ii),
1000x – x = 30219. bar 219 – 30. bar 219
∴ 999x = 30189
