Time conversion between decimal and hours, minutes and seconds examples are presented with their detailed solutions. More questions with solutions are presented at the bottom of the page.
The steps suggested here takes into account all conversions, with clear explanations that may be used in more challenging situations.
Table of Conversion and Factor of Conversion
The table shown below is used to make conversions of time.
1) 1 minute = 60 seconds
2) 1 hour = 60 minutes
3) 1 hour = 3600 seconds
The abbreviations: hrs = hour, min = minutes and sec = seconds will be used in what follows.
Using 1) above and divide both sides by 1 min or by 60 sec, we obtain two factor 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 divide both sides by 1 hr or by 60 min, we obtain two factors of conversion between hours and mninutes 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 divide 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.
Solution to Example 1
The time given may be written as
\[ \color{red}{6 \text{ hrs}} + 56 \text{ min} + 45 \text{ sec} \quad (1) \]
Find how many hours 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
\[ 45 \text{ sec} = 45 \cancel{\text{sec}} \times \displaystyle \frac{1 \text{ hrs}}{3600 \cancel{\text{ sec}}} \]
Simplify and evaluate
\[ 45 \text{ sec} = \displaystyle \frac{1 \text{ hrs}}{3600 } = \frac{45 \times 1 \text{ hrs}}{3600} = \color{red}{0.0125 \text{ hrs}} \]
Example 3
Convert the time \( \text{12:05:52} \) into its decimal form and round answer to two decimal places.
Solution to Example 3
The given time may be written as
\[ \text{12:05:52} = 12 \text{ hrs} + 5 \text{ min} + 52 \text{ sec} \]
In one step we convert \( 5 \text{ min} \) and \( 52 \text{ sec} \) into \( \text{ hrs} \) using the factors of conversion \( \displaystyle \frac{1 \text{ hrs}}{60 \text{ min}} \) and \( \displaystyle \frac{1 \text{ hrs}}{3600 \text{ sec}} \) as follows:
\[ \text{12:05:52} = 12 \text{ hrs} + 5 \text{ min} \times \displaystyle \frac{1 \text{ hrs}}{60 \text{ min}} + 52 \text{ sec} \times \frac{1 \text{ hrs}}{3600 \text{ sec}}\]
Cancel \( \text{ min} \) and \( \text{ sec} \)
\[ \text{12:05:52} = 12 \text{ hrs} + 5 \cancel{\text{ min}} \times \displaystyle \frac{1 \text{ hrs}}{60 \cancel{\text{ min}}} + 52 \cancel{\text{ sec}} \times \frac{1 \text{ hrs}}{3600 \cancel{\text{ sec}}}\]
Simplify, evaluate and round to two decimal places
\[ \text{12:05:52} = 12 \text{ hrs} + \displaystyle \frac{ 5 \times 1 \text{ hrs}}{60 } + \frac{ 52 \times 1 \text{ hrs}}{3600 } = 12.10 \text{ hrs}\]
Example 4
Convert the time \( 9.36 \text{ hrs} \) to the form \( \text{hh:mm:ss} \).
Solution to Example 4
The given time may be written as
\[ 9.36 \text{ hrs} = \color{red}{9 \text{ hrs}} + 0.36 \text{ hrs} \]
Convert \( 0.36 \text{ hrs} \) into minutes using the factor of conversion \( \displaystyle \frac{60 \text{ min}} {1 \text{ hrs}} \) as follows
\[ 0.36 \text{ hrs} = 0.36 \text{ hrs} \times \displaystyle \frac{60 \text{ min}} {1 \text{ hrs}} \]
Cancel \( \text{ hrs} \) on the right
\[ 0.36 \text{ hrs} = 0.36 \cancel {\text{ hrs}} \times \displaystyle \frac{60 \text{ min}} {1 \cancel {\text{ hrs}}} \]
Simplify and evaluate
\[ \displaystyle 0.36 \text{ hrs} = \frac{0.36 \times 60 \text{ min}} {1} = 21.6 \text{ min}\]
\( 21.6 \text{ min} \) may be written as
\[ 21.6 \text{ min} = \color{red}{21 \text{ min}} + 0.6 \text{ min} \]
Convert \( 0.6\text{ min} \) into seconds using the factor of conversion \( \displaystyle \frac{60 \text{ sec}} {1 \text{ min}} \) as follows
\[ 0.6 \text{ min} = 0.6 \text{ min} \times \displaystyle \frac{60 \text{ sec}} {1 \text{ min}} \]
Cancel \( \text{ min} \) on the right
\[ 0.6 \text{ min} = 0.6 \cancel{\text{ min}} \times \displaystyle \frac{60 \text{ sec}} {1 \cancel{\text{ min}}} \]
Simplify and evaluate
\[ 0.6 \text{ min} = \displaystyle \frac{0.6 \times 60 \text{ sec}} {1} = \color{red}{36 \text{ sec}} \]
Hence
\[ 9.36 \text{ hrs} = \color{red}{\text{9:21:36}}\]
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 \( \text{hh:mm:ss} \).
Solution to Example 5
a)
To convert seconds into decimal hours, use the factor of conversion \( \displaystyle \frac{1 \text{ hrs}}{3600 \text{ sec} } \) as follows
\[ 34520 \text{ sec} = 34520 \text{ sec} \times \displaystyle \frac{1 \text{ hrs}}{3600 \text{ sec} } \]
Cancel \( \text{ sec} \) on the right
\[ 34520 \text{ sec} = 34520 \cancel{\text{ sec}} \times \displaystyle \frac{1 \text{ hrs}}{3600 \cancel{\text{ sec}} } \]
Simplify, evaluate and round to two decimal places
\[ 34520 \text{ sec} = \displaystyle \frac{34520 \times 1 \text{ hrs}}{3600 } = 9.58888 \text{ hrs} \]
Round to two decimal places
\[ 34520 \text{ sec} = 9.59 \text{ hrs} \]
b)
To convert seconds into decimal minutes, use the factor of conversion \( \displaystyle \frac{1 \text{ min}}{60 \text{ sec}} \) as follows
\[ 34520 \text{ sec} = 34520 \text{ sec} \times \displaystyle \frac{1 \text{ min}}{60 \text{ sec} }\]
Cancel \( \text{ sec} \) on the right
\[ 34520 \text{ sec} = 34520 \cancel{\text{ sec}} \times \displaystyle \frac{1 \text{ min}}{60 \cancel{\text{ sec}}} \]
Simplify, evaluate and round to two decimal places
\[ 34520 \text{ sec} = \displaystyle \frac{34520 \times 1 \text{ min}}{60 } = 575.33 \text{ min} \]
c)
In part a) we found that the given time may be written as
\[ 34520 \text{ sec} = 9.58888 \text{ hrs} \]
One way to write the given time in the form \( \text{hh:mm:ss} \), follow the steps in example 2 or example 4 to convert \( 9.59 \text{ hrs} \) of the \( \text{hh:mm:ss} \)
\[ 34520 \text{ sec} = 9.58888 \text{ hrs} = 9:35:20\]
Questions
Use table 1 above to determine the factor of conversion \( R \) and convert.
Convert \( \quad 234 \text{ min} \) to a) seconds , b) decimal hours , c) to the form \( \; \text{hh:mm:ss} \)
Convert \( \quad 2.05 \text{ hrs} \) to a) minutes , b) seconds
Convert \( \quad 11055 \text{ sec} \) to a) decimal hours , b) decimal minutes, c) to the form \( \; \text{hh:mm:ss} \)
c)
Use the steps in example 2 or 4 to convert the decimal hours found in part b) to the form \( \; \text{hh:mm:ss} \)
\[ \quad 234 \text{ min} = 3.9 \text{ hrs} = \text{3:54:00} \]
c)
Use the steps in example 2 or 4 to convert the decimal hours found in part a) to the form \( \; \text{hh:mm:ss} \)
\[ \quad 11055 \text{ sec} = 3.07083 \text{ hrs} = \text{3:04:15} \]
