Question

What is 1 and 29/40 as a decimal

Answer 1

`1+\frac { 29 }{ 40 } \\ \\ =\frac { 40 }{ 40 } +\frac { 20 }{ 40 } +\frac { 9 }{ 40 } \\ \\ =1+\frac { 1 }{ 2 } +\frac { 9 }{ 4 } \cdot \frac { 1 }{ 10 } \\ \\ =1+\frac { 1 }{ 2 } +\left( \frac { 8 }{ 4 } +\frac { 1 }{ 4 } \right) \cdot \frac { 1 }{ 10 } \\ \\ =1+\frac { 1 }{ 2 } +\left( 2+\frac { 1 }{ 4 } \right) \cdot \frac { 1 }{ 10 } \\ \\ =1+\frac { 1 }{ 2 } +\frac { 2 }{ 10 } +\frac { 1 }{ 4 } \cdot \frac { 1 }{ 10 } \\ \\ =1.000+0.500+0.200+0.025\\ \\ =1.725`

Answer 2

`1(29)/(40)=1(29\cdot2)/(40\cdot2)=1(58)/(80)\ :(\\\dots\\1(29)/(40)=1(29\cdot5)/(40\cdot5)=1(145)/(200)\ ?... hmm\ 1(145)/(200)=1(145\cdot5)/(200\cdot5)=1(725)/(1,000)\ \ hooray\ :)\\\\\huge\boxed{1(29)/(40)=1(29\cdot25)/(40\cdot25)=1(725)/(1,000)=\boxed{1.725}}`