Question

23 degrees 20’48 is the same as _degrees.

Answer 1

`\large\boxed{23^o20'48''=\left(23(26)/(75)\right)^o}`

Explanation:

`\text{We know:}\\\\1^o=60'\to1'=\left((1)/(60)\right)^o\\\\1'=60''\to1^o=(60)(60'')=3600''\to1''=\left((1)/(3600)\right)^o\\\\23^o20'48''\\\\20'=\left((20)/(60)\right)^o=\left((1)/(3)\right)^o\\\\48''=\left((48)/(3600)\right)^o=\left((1)/(75)\right)^o\\\\\text{Therefore}\\\\23^o20'48''=23^o+20'+48''=23^o+\left((1)/(3)\right)^o+\left((1)/(75)\right)^o\\\\=\left(23+(1\cdot25)/(3\cdot75)+(1)/(75)\right)^o=\left(23+(25)/(75)+(1)/(75)\right)^o=\left(23(26)/(75)\right)^o`