Question

[Lê Thu Hiền]

1) Chứn tỏ rằng:

a) 0,(32)+0,(67)=1

b) 0,(33)x3=1

@

2) Tìm x:

0,(12):1,(6)=x:0,(3)

Answer 1

[Nguyễn Tiến Dũng]

1)

a)\(0,\left(32\right)+0,\left(67\right)\)

\(=0,\left(01\right).32+0,\left(01\right).67\)

\(=0,\left(01\right).\left(32+67\right)\)

\(=\frac{1}{99}.99\)

\(=1\left(đpcm\right)\)

b)\(0,\left(33\right).3\)

\(=0,\left(01\right).33.3\)

\(=\frac{1}{99}.33.3\)

\(=\frac{33}{99}.3\)

\(=\frac{99}{99}\)

\(=1\left(đpcm\right)\)

2)\(0,\left(12\right):1,\left(6\right)=x:0,\left(3\right)\)

\(\left[\left(0,01\right).12\right]:\left[1+0,\left(6\right)\right]=x:\left[0,\left(1\right).3\right]\)

\(\left(\frac{1}{99}.12\right):\left[1+0,\left(1\right).6\right]=x:\left(\frac{1}{9}.3\right)\)

\(\frac{4}{33}:\left[1+\frac{1}{9}.6\right]=x:\frac{1}{3}\)

\(\frac{4}{33}:\left[1+\frac{2}{3}\right]=x.3\)

\(3x=\frac{4}{33}:\frac{5}{3}\)

\(3x=\frac{4}{33}\cdot\frac{3}{5}\)

\(3x=\frac{4}{55}\)

\(x=\frac{4}{55}:3\)

\(x=\frac{4}{55}\cdot\frac{1}{3}\)

\(x=\frac{4}{165}\)