# Time Conversion Examples with Solutions

 $\require{cancel}$ $\require{bbox}$

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
$45 \text{ sec} = \displaystyle \frac{1 \text{ hrs}}{3600 } = \frac{45 \times 1 \text{ hrs}}{3600} = \color{red}{0.0125 \text{ hrs}}$

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"
$56 \text{ min} = 56 \cancel {\text{ min}} \times \displaystyle \frac{1 \text{ hrs}}{60 \cancel {\text{ min}} }$
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
$\bbox[10px, border: 2px solid red] { \text{6:56:45} = \color{red}{ 6.95 \text{ hrs} }}$
An online calculator to convert time from hrs, min and sec to Decimal may be used for more practice.

## Convert Decimal Form to dd:hh:mm:ss

Example 2
Convert $2.34 \text{ hrs}$ the form $\text{hh:mm:ss}$.

Solution to Example 2
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
$0.34 \text{ hrs} = 0.34 \cancel{\text{ hrs}} \times \displaystyle \frac{60 \text{ min}} {1 \cancel{\text{ hrs}} }$
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
$0.4 \text{ min} = 0.4 \cancel{\text{ min}} \times \displaystyle \frac{60 \text{ sec}} {1 \cancel{\text{ min}}}$
Simplify and evaluate
$0.4 \text{ min} = \displaystyle \frac{0.4 \times 60 \text{ sec}} {1 } = \color{red}{24 \text{ sec}}$
Hence
$\bbox[10px, border: 2px solid red] { 2.34 \text{ hrs} = \color{red}{\text{2:20:24}}}$
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 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 table 1 above to determine the factor of conversion $R$ and convert.

1. Convert $\quad 234 \text{ min}$ to   a) seconds ,   b) decimal hours ,   c) to the form $\; \text{hh:mm:ss}$
2. Convert $\quad 2.05 \text{ hrs}$ to   a) minutes ,   b) seconds
3. Convert $\quad 11055 \text{ sec}$ to   a) decimal hours ,   b) decimal minutes,   c) to the form $\; \text{hh:mm:ss}$
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