# How do you evaluate the following expression using decimals?:  4.136 - 8.2612 + 77/64 + 205/128

$4.136 - 8.2612 + \frac{77}{64} + \frac{205}{128} = - 1.3205125$
Here $\frac{77}{64}$ and $\frac{205}{128}$ have only $2$ as prime factors for denominators. In fact they are ${2}^{6}$ and ${2}^{7}$ and hence they can be converted into decimal form by multiplying numerator and denominator by ${5}^{6} = 15625$ and ${5}^{7} = 78125$.
Hence $\frac{77}{64} = 1.203125$ and $\frac{205}{128} = 1.6015625$.
Hence $4.136 - 8.2612 + 1.203125 + 1.6015625 = - 1.3205125$