Decimal Fraction - 01

Explanation:-

$$\eqalign{ & 3.\overline {87} - 2.\overline {59} \cr & = \left( {3 + 0.\overline {87} } \right) - \left( {2 + 0.\overline {59} } \right) \cr & = \left( {3 + \frac{{87}}{{99}}} \right) - \left( {2 + \frac{{59}}{{99}}} \right) \cr & = 1 + \left( {\frac{{87}}{{99}} - \frac{{59}}{{99}}} \right) \cr & = 1 + \frac{{28}}{{99}} \cr & = 1.\overline {28} \cr}$$

Explanation:-

$$\eqalign{ & \frac{{0.0203 \times 2.92}}{{0.0073 \times 14.5 \times 0.7}} \cr & = \frac{{203 \times 292}}{{73 \times 145 \times 7}} \cr & = \frac{4}{5} \cr & = 0.8 \cr}$$

Explanation:-

$$\eqalign{ & 101\frac{{27}}{{100000}} \cr & = 101 + \frac{{27}}{{100000}} \cr & = 101 + .00027 \cr & = 101.00027 \cr}$$

Explanation:-

$$\eqalign{ & 6.\overline {46} \cr & = 6 + 0.\overline {46} \cr & = 6 + \frac{{46}}{{99}} \cr & = \frac{{594 + 46}}{{99}} \cr & = \frac{{640}}{{99}} \cr}$$

Explanation:-

Sum of decimal places = 7.
Since the last digit to the extreme right will be zero (since 5 x 4 = 20), so there will be 6 significant digits to the right of the decimal point.

Explanation:-

$$\eqalign{ & 1 \div 0.2 = \frac{1}{{0.2}} = \frac{{10}}{2} = 5; \cr & 0.\overline 2 = 0.222...; \cr & {\left( {0.2} \right)^2} = 0.04 \cr & 0.04 < 0.2 < 0.22.... < 5 \cr & {\text{Since}}\,0.04\,{\text{is}}\,{\text{the}}\,{\text{least,}}\,{\text{so}}\,{\left( {0.2} \right)^2}\,{\text{is}}\,{\text{the}}\,{\text{least}}. \cr}$$

Explanation:-

3.14 x 10⁶ = 3.14 x 1000000 = 3140000.

Explanation:-

$$\eqalign{ & \,\,\,\,34.95 \cr & \,240.016 \cr & + 23.98 \cr & - - - - - \cr & 298.946 \cr & - - - - - \cr}$$

Explanation:-

2 x 5 = 10.
Sum of decimal places = 4
∴ 0.002 x 0.5 = 0.001

Explanation:-

$$\eqalign{ & 617.00 \cr & \,\,\,\,\,\,\,6.017 \cr & \,\,\,\,\,\,\,0.617 \cr & + \,\,\,6.0017 \cr & - - - - - - \cr & \,\,\,629.6357 \cr & - - - - - - \cr}$$