Table of Conversion and Factor of Conversion
The table shown below is used to make conversions of time:
- 1 minute = 60 seconds
- 1 hour = 60 minutes
- 1 hour = 3600 seconds
The abbreviations: hrs = hour, min = minutes, and sec = seconds will be used in what follows.
Using 1) above and dividing both sides by 1 min or by 60 sec, we obtain two factors of conversion between minutes and seconds given by:
\[ \color{red}{\frac{1 \text{ min}}{60 \text{ sec}} = 1} \quad (I) \]or
\[ \color{red}{\frac{60 \text{ sec}}{1 \text{ min}} = 1} \quad (II) \]Using 2) above and dividing both sides by 1 hr or by 60 min, we obtain two factors of conversion between hours and minutes given by:
\[ \color{red}{\displaystyle \frac{1 \text{ hrs}}{60 \text{ min}} = 1} \quad (III) \]or
\[ \color{red}{\displaystyle \frac{60 \text{ min}}{1 \text{ hrs}} = 1} \quad (IV) \]Using 3) above and dividing both sides by 1 hr or by 3600 sec, we obtain two factors of conversion between hours and seconds given by:
\[ \color{red}{\displaystyle \frac{1 \text{ hrs}}{3600 \text{ sec}} = 1} \quad (V) \]or
\[ \color{red}{\displaystyle \frac{3600 \text{ sec}}{1 \text{ hrs}} = 1} \quad (VI) \]Note that all factors of conversion are equal to \( 1 \) and may therefore be used in multiplications without changing the value.
Convert \( \text{hh:mm:ss} \) to Decimal Form
Example 1
Convert \( \text{6:56:45} \) to a decimal form and round to two decimal places.
View Solution
The time given may be written as:
\[ \color{red}{6 \text{ hrs}} + 56 \text{ min} + 45 \text{ sec} \quad (1) \]Find how many hours are in 45 seconds starting as follows:
\[ 45 \text{ sec} = 45 \text{ sec} \times 1 \]Substitute \( 1 \) by the factor of conversion \( \displaystyle \frac{1 \text{ hrs}}{3600 \text{ sec}} \):
\[ 45 \text{ sec} = 45 \text{ sec} \times \displaystyle \frac{1 \text{ hrs}}{3600 \text{ sec}} \]Cancel \( \text{sec} \) on the right side, simplify, and evaluate:
\[ 45 \text{ sec} = \frac{45 \times 1 \text{ hrs}}{3600} = \color{red}{0.0125 \text{ hrs}} \]Find how many hours are in 56 minutes:
\[ 56 \text{ min} = 56 \text{ min} \times 1 \]Substitute \( 1 \) by the factor of conversion \( \displaystyle \frac{1 \text{ hrs}}{60 \text{ min}} \):
\[ 56 \text{ min} = 56 \text{ min} \times \displaystyle \frac{1 \text{ hrs}}{60 \text{ min}} \]Cancel "min", simplify, and evaluate:
\[ 56 \text{ min} = 56 \times \displaystyle \frac{1 \text{ hrs}}{60} = \color{red}{0.93333333333 \text{ hrs}} \]We now convert by substituting minutes and seconds to hours in the addition \( (1) \) above:
\[ 6:56:45 = \color{red}{6 \text{ hrs} + 0.93333333333 \text{ hrs} + 0.0125 \text{ hrs}} = 6.94583333333 \text{ hrs} \]Round to two decimal places:
An online calculator to convert time from hrs, min and sec to Decimal may be used for more practice.
Convert Decimal Form to hh:mm:ss
Example 2
Convert \( 2.34 \text{ hrs} \) to the form \( \text{hh:mm:ss} \).
View Solution
The time given may be written as:
\[ 2.34 \text{ hrs} = \color{red}{2 \text{ hrs}} + 0.34 \text{ hrs} \]Convert \( 0.34 \text{ hrs} \) into minutes using the factor of conversion \( \displaystyle \frac{60 \text{ min}}{1 \text{ hr}} \):
\[ 0.34 \text{ hrs} = 0.34 \text{ hrs} \times 1 = 0.34 \text{ hrs} \times \displaystyle \frac{60 \text{ min}}{1 \text{ hrs}} \]Cancel \( \text{hrs} \) on the right, simplify, and evaluate:
\[ 0.34 \text{ hrs} = \displaystyle \frac{0.34 \times 60 \text{ min}}{1} = 20.4 \text{ min} \]\( 20.4 \text{ min} \) may be written as:
\[ 20.4 \text{ min} = \color{red}{20 \text{ min}} + 0.4 \text{ min} \]Convert \( 0.4 \text{ min} \) into seconds using the factor of conversion \( \displaystyle \frac{60 \text{ sec}}{1 \text{ min}} \):
\[ 0.4 \text{ min} = 0.4 \text{ min} \times 1 = 0.4 \text{ min} \times \displaystyle \frac{60 \text{ sec}}{1 \text{ min}} \]Cancel \( \text{min} \) on the right side, simplify, and evaluate:
\[ 0.4 \text{ min} = \displaystyle \frac{0.4 \times 60 \text{ sec}}{1} = \color{red}{24 \text{ sec}} \]Hence:
An online calculator to convert time from decimal to hrs, min and sec may be used for more practice.
Examples with Solutions
Example 3
Convert the time \( \text{12:05:52} \) into its decimal form and round the answer to two decimal places.
Example 4
Convert the time \( 9.36 \text{ hrs} \) to the form \( \text{hh:mm:ss} \).
Example 5
Convert \( 34520 \text{ sec} \) into:
a) decimal hours (round to two decimal places)
b) decimal minutes (round to two decimal places)
c) the form \( \text{hh:mm:ss} \).
Questions
Use the conversion table above to determine the factor of conversion and convert:
- Convert \( 234 \text{ min} \) to a) seconds, b) decimal hours, c) the form \( \text{hh:mm:ss} \)
- Convert \( 2.05 \text{ hrs} \) to a) minutes, b) seconds
- Convert \( 11055 \text{ sec} \) to a) decimal hours, b) decimal minutes, c) the form \( \text{hh:mm:ss} \)