We've already looked at how to find angles using trigonometric ratios and we are used to giving our answers as whole numbers or decimals. Now we are going to look at another way to express a part of a degree using minutes and seconds.
There are $60$60 minutes in $1$1 degree.
There are $60$60 seconds in $1$1 minute.
Converting decimals to minutes and seconds
To convert a number in decimal form into minutes and seconds, we need first to find what number out of $60$60 the decimal part of the number represents.
For example, let's say we wanted to round $15.72^\circ$15.72° to the nearest minute.
We need to work out $15^\circ$15° + $0.72$0.72 of a degree, which is $15^\circ$15° plus $0.72$0.72 of $60$60 minutes.
| $0.72\times60$0.72×60 | $=$= | $43.2$43.2 minutes |
So, $15.72^\circ$15.72° rounded to the nearest minute is $15^\circ$15°$43$43'.
Converting on a calculator
There are also some buttons our your calculator to help you work with minutes and seconds.
The button highlighted in blue allows you to write degrees and minutes in your calculator.
The button highlighted in green will convert between decimals and minutes/seconds.
Rounding
Rounding minutes and seconds is similar to rounding decimals. However, because there are $60$60 minutes in a degree and $60$60 seconds in a minute, our half way point is $30$30.
- If the minutes are below $30$30, we round down to the nearest degree.
- If the minutes are $30$30 or above, we round up to the nearest degree.
- If the seconds are below $30$30, we round down to the nearest minute.
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If the seconds are $30$30 or above, we round up to the nearest minute.
Worked Examples
Question 1
Round $25^\circ$25°$49$49'$40$40" to the nearest minute.
$\editable{}$° $\editable{}$'
Question 2
Convert the following into degrees and minutes:
$24.4^\circ$24.4°=$\editable{}$ degrees $\editable{}$ minutes
Question 3
Question 4
Consider the following diagram.
Find the value of $x$x correct to 2 decimal places.
Hence find $x$x to the nearest minute.