Sexagesimal

Sexagesimal is a numeral system in which each unit is divided into 60 units of lower order, that is to say, it is a base-60 number system

The sexagesimal system was used by the Sumerians and Babylonians. It is currently used to measure time and angles.

1 h flecha 60 min flecha 60 s

1º  flecha 60'       flecha 60''


Converting Sexagesimal into Decimal Form

Convert 3 hours, 36 minutes, 42 seconds to seconds.

Sexagesimal Decimal Conversion

Converting Decimal into Sexagesimal Form

1To convert to major units, divide.

7,520''

Sexagesimal Decimal Conversion

2To convert to minor units, multiply.

Sexagesimal Decimal Conversion


For the measurement of time and angles, the following steps can be performed:

Addition

1.

Place the hours under the hours (or the degrees under the degrees), the minutes under the minutes and the seconds under the seconds and add together.

Sexagesimal Addition

2.

If the seconds total more than 60, they are divided by 60, the remainder will remain in the seconds column and the quotient is added to the minutes column.

Sexagesimal Addition

3.

Repeat the same process for the minutes.

Sexagesimal Addition

Subtraction

1.

Place the hours under the hours (or the degrees under the degrees), the minutes under the minutes and seconds under seconds and subtract.

Sexagesimal Subtraction

2.

If it is not possible to subtract the seconds, convert a minute of the minuend into 60 seconds and add it to the minuend seconds. Then, the subtraction of the seconds will be possible.

Sexagesimal Subtraction

3.

Repeat the same process for the minutes.

Sexagesimal Subtraction

Multiplication by a Number

1.

Multiply the seconds, minutes and hours (or degrees) by number.

Sexagesimal Multiplication

2.

If the seconds exceed 60, divide that number by 60, the remainder will remain in the the seconds column and the quotient is added to the minutes column.

Sexagesimal Multiplication

3.

Repeat the same process for the minutes.

Sexagesimal Multiplication

Division by a number

Divide 37º 48' 25'' by 5.

1.

Divide the hours (or degrees) by the number.

Sexagesimal Division

2.

The quotient becomes the degrees and the remainder becomes the minutes when multiplied by 60.

Sexagesimal Division

3.

Add these minutes to the minutes column and repeat the same process for the minutes.

Sexagesimal Division

4.

Add these seconds to the seconds column and then divide the seconds by the number.

Sexagesimal Division