Decimal degrees are used to represent longitude and latitude geographic coordinates as fractions in decimals. Its main application is in web mapping as in GPS devices and open-street map. They are an alternate form of degree, minutes, and seconds (DMS).

**i) ** Stepwise illustration of converting decimal degrees (DD) to decimals minutes and seconds (DMS) with the help of an example:

**Example: **Convert decimal degrees 8.23456 (DD) into degrees, minutes, and seconds (DMS)

**Solution** – Step 1: Subtract the whole degrees.

8.23456 – 8 = 0.23456 (8 is the whole number)

Step 2: Convert the fractional degree into minutes by multiplying the decimal part of the degree by 60. The whole number that we get is the minutes

$0.23456$ $\times$ $60’$ per degree = $14.0736’$

Step 3: Similarly, we subtract the whole minutes from the fractional minutes we found out

$14.0726’$ $-\ 14$ = 0$.0726’$ (14 is the whole minutes)

Step 4: Convert the fractional minutes into seconds by multiplying the decimal part of the minutes by 60. The whole number that we get is the seconds. The decimal part of the second is no more converted and stays as the decimal seconds.

$0.0726\ \times\ 60$ = $4.356’’$

So, the decimal, minutes, seconds that we get is $8^o\ 14’\ 4.356’’$

**i****i) ** Stepwise illustration of converting decimals minutes and seconds (DMS) to decimal degrees (DD) with the help of an example:

**Example:** Convert decimal minutes and seconds $25^o\ 8’\ 10’’$ (DMS) into decimal degrees (DD)

**Solution** – Step 1: Convert the seconds to minutes. We know that 60’’ is equal to 1’. Therefore, 10’’ is equal t 10/60 = 0.167’ (minutes)

Step 2: Add the decimal minutes to the whole minutes. The whole minutes is 8 given and we found out the decimal minutes to be 0.167. So, the total minutes would be $8\ +\ 0.167$ = $8.167‘$

Step 3: Convert the minutes to degrees. We know that 60’ is equal to $1^o$. Therefore, $8.167’$ is equal to $\frac{8.167}{60}$ = $0.1361^o$

Step 4: Add the decimal degrees to the whole degrees. The whole degree is $25$ and the decimal degrees is $0.1361$. So, the total degrees is $25\ +\ 0.1361$ = $25.1361^o$

So, the decimal degree that we get is $25.1361^o$ (DD).