Video Transcript
Jacob converted 152.455 degrees to
degrees, minutes, and seconds. His answer was 152 degrees, 26
minutes, and 78 seconds. Which of the following is
correct? Option (A) the correct answer is
152 degrees, 45 minutes, and 60 seconds. Option (B) the correct answer is
152 degrees, 27 minutes, and 18 seconds. Option (C) Jacob’s answer is
correct because 152 plus 26 divided by 60 plus 78 divided by 3600 equals
152.455. Option (D) Jacob’s answer is
correct because 152 plus 26 divided by 60 plus 78 divided by 60 equals 152.455. Or option (E) Jacob’s answer is
correct because 152 plus 26 divided by 3600 plus 78 divided by 60 equals
152.455.
In this question, we have a value,
152.455, which is a decimal degrees value. We are told that this has been
converted to the value 152 degrees, 26 minutes, and 78 seconds. So let’s see if this is
correct. To check this, let’s recall how to
convert a decimal degrees value into one in degrees, minutes, and seconds.
Firstly, we can recall that the
whole part of the number representing the decimal degrees is the whole number of
degrees. We can take the given value,
152.455 degrees, and see that the whole number part is 152. So we know that the degrees,
minutes, and seconds value has a degrees value of 152 degrees.
The second stage of the conversion
is to multiply the decimal part of our value by 60 to give the number of
minutes. The decimal part is 0.455, so we
multiply 0.455 by 60. This gives us the number of
minutes. But notice that this is not a whole
number. If it was a whole number, there
would be zero seconds. However, we take the whole number
here as our number of minutes. So that’s 27 minutes. And we use the decimal part of this
number to work out the number of seconds.
Part three of the conversion tells
us that if the number of minutes, which we had here as 27.3, has a decimal part,
then multiply the decimal part by 60 to give the number of seconds. The decimal part is 0.3, and 0.3
times 60 is 18. That means that the number of
seconds is 18. This is a whole number, but note
that if this was a decimal, we could now round the seconds part of this to an
appropriate degree of accuracy.
We can therefore say that 152.455
degrees is equivalent to 152 degrees, 27 minutes, and 18 seconds. The correct statement is option
(B). But before we finish with this
question, let’s consider a few of the other answer options and why they might be a
little confusing.
Options (C), (D), and (E) look like
they use something like the process we use to convert a value in degrees, minutes,
and seconds into a value in decimal degrees. Let’s review how we can convert the
opposite way than we previously did, that is, from degrees, minutes, and seconds to
a decimal degrees value. If we consider a given value as 𝑑
degrees, 𝑚 minutes, and 𝑠 seconds, then this is equal to 𝑑 plus 𝑚 over 60 plus
𝑠 over 3600 degrees.
Let’s look at Jacob’s answer of 152
degrees, 26 minutes, and 78 seconds. To convert this value, we would
have 152 plus 26 over 60 plus 78 over 3600. This is the process followed in
option (C). And when we perform the
calculation, we do indeed get a decimal answer of 152.455 degrees, which was the
value that Jacob started with. So how can these two different
values produce the same decimal degrees value?
To answer this, let’s recall that
one degree is made up of 60 minutes and one minute is made of 60 seconds. Consider that here we have 78
seconds. 78 seconds is equivalent to one
minute and 18 seconds. We can then write 26 minutes 78
seconds as 27 minutes and 18 seconds. So both these values are
equivalent. But which is the correct form? Well, just as we wouldn’t describe
a time as 26 minutes and 78 seconds — we would describe it as 27 minutes and 18
seconds — we follow the same notation for that of degrees, minutes, and seconds. And so we can confirm that the
correct statement is that given in option (B).
