Question

1.представьте в виде обыкновенной дроби число 0,1(42)?

2. Вычислите:
5,4(6) - 3,(3) =
2,7(6) - 1,2(38) =

Answer 1

0,1(42)=(142-1)/990=141/990=47/330

5,4(6) - 3,(3) =2,1(3)
2,7(6) - 1,2(38) =1,5(28)

Answer 2

1. 

0,1(42) = (142 -1)/990 = 141/990 = 47/330

2.

5,4(6) – 3,(3) = 5 + (46 – 4)/90 – (3 + (3 – 0)/9) =  5 + 42/90 – 3 -  3/9 =

= 2 + 14/30 – 1/3 = 2  + 4/30 = 2⁴/₃₀ = 2,1(3)

2,7(6) – 1,2(38) = 2 + (76 – 7)/90 – (1 + (238 – 2)/990) =

=  2 + 69/90 – 1 – 236/990 = 1 + 759/990 -  236/990 = 1 +  523/990 = 

= 1⁵²³/₉₉₀ = 1,5(28)