Without using a calculator, write
20 degrees, 30 minutes, 45 seconds in degrees.
We recall that the quotation mark
symbols in the question represent minutes and seconds, respectively. There are 60 minutes in one
degree. This means that in order to convert
from minutes to degrees, we need to divide by 60. Likewise, there are 60 seconds in
one minute. 60 multiplied by 60 is 3600. Therefore, this is the number of
seconds in one degree. To convert from seconds to degrees,
we need to divide by 3600. We need to write the three parts of
our original number separately.
We begin with 20 degrees. We then have 30 minutes, which in
degrees would be 30 divided by 60 or 30 over 60. We then have 45 seconds, which can
be converted into degrees by dividing by 3600. The first fraction simplifies to
three over six and then one-half. One-half is equal to 0.5. So, 30 divided by 60 is 0.5. We know that 45 multiplied by eight
is 360. This means that 45 multiplied by 80
is 3600. So, our second fraction simplifies
to one over 80 or one eightieth. We recall that one-eighth is equal
to 0.125. It is half of a quarter. Dividing this by 10 gives us that
one eightieth is equal to 0.0125. Adding these three values gives us
20.5125. We can, therefore, conclude that 20
degrees, 30 minutes, and 45 seconds is the same as 20.5125 degrees.