convert 36°54 into sexagesimal seconds
Answers
Answer:
Step-by-step explanation:
First, we will divide 7250 by 60 to get seconds like this
\begin{array}{ccccccccccc} & & 125&\\ \cline{3-10} \multicolumn{2}{r}{60 \surd} & 7520&& \\ & &7500& & & & \\ \cline{3-7} \cline{6-10} & &20&&\\ \end{array}
Step 2
The remainder 20 represents seconds and the quotient 125 will be divided by 60 further to get hours and minutes:
\begin{array}{ccccccccccc} & & 2&\\ \cline{3-10} \multicolumn{2}{r}{60 \surd} & 125&& \\ & &120& & & & \\ \cline{3-7} \cline{6-10} & &5&&\\ \end{array}
The remainder 5 represents minutes and the quotient 2 reflects hours. Hence, the final answer is:
7520'' = 2^o 5' 20''
2 Convert 12,900'' into degree, minutes and seconds
We know that in one hour there are 60 minutes and in one minute there are 60 seconds. Hence, in one hour, there are 3600 (60 x 60) seconds. To get the hours and minutes, we will use the division operation twice.
Step 1
First, we will divide 12,900 by 60 like this:
\begin{array}{ccccccccccc} & & 215&\\ \cline{3-10} \multicolumn{2}{r}{3600 \surd} & 12900&& \\ & &12900& & & & \\ \cline{3-7} \cline{6-10} & &0&&\\ \end{array}
Step 2
The remainder zero represents the seconds and the quotient 215 will be further divided by 60 to get minutes and hours like this:
\begin{array}{ccccccccccc} & & 3&\\ \cline{3-10} \multicolumn{2}{r}{60 \surd} & 215&& \\ & &180& & & & \\ \cline{3-7} \cline{6-10} & &35&&\\ \end{array}
The remainder 35 represents the minutes and the quotient 3 reflects hours. We will write the final answer like this:
12,900'' = 3^o 35'
To convert the larger units to smaller units, we will use the operation of multiplication. Consider the following examples.
1 Convert 95.62 in degree minute and seconds
95 is a degree because it is the whole number part. Let us find minutes and seconds.0.62 x 60 = 37.2. Again, the whole number part 37 will be considered as minutes. Now, we will multiply 0.2 with 60 to get seconds.0.2 x 60 = 12 seconds. Hence, we will write the decimal number 95.62 in degree, minutes and seconds like this:
95.62 = 95^o 37 ^ {'} 12 ^ {''}
2 Convert 48.27 in degree minute and seconds
48 is a degree because it is the whole number part. Let us find minutes and seconds.
0.27 x 60 = 16.2
Again, the whole number part 16 will be considered as minutes. Now, we will multiply 0.2 with 60 to get seconds.
0.2 x 60 = 12 seconds
Hence, we will write the decimal number 48.27 in degree, minutes and seconds like this:
48.27 = 48^o 16 ^ {'} 12 ^ {''}
3 Convert 82.27 in degree minute and seconds
82 is a degree because it is the whole number part. Let us find minutes and seconds.
0.27 x 60 = 16.2
Again, the whole number part 16 will be considered as minutes. Now, we will multiply 0.2 with 60 to get seconds.
0.2 x 60 = 12 seconds
Hence, we will write the decimal number 95.62 in degree, minutes and seconds like this:
82.27 = 82^o 16 ^ {'} 12 ^ {''}
Operations with Sexagesimal Numbers
We can add, subtract, multiply and divide numbers in sexagesimal form. We will discuss each operation below one by one with the examples.
Addition
Add 29 ^ o 36'' 28' and 54^o 45'' 54'.
Follow these steps to add the above two numbers.