Question: For about 10 years after the French Revolution, the French government attempted to base measures of time on multiples of ten: One week consisted of 10 days, one day consisted of 10 hours, one hour consisted of 100 minutes, and one minute consisted of 100 seconds. What are the ratios of (a) the French decimal week to the standard week and (b) the French decimal second to the standard second?

One week consisted of 10 days.

One day consisted of 10 hours.

One hour consisted of 100 minutes.

One minute consisted of 100 seconds.

Decimal time is nothing but the representation of the time of day using decimally related units which refers to the time system used in France.

The ratio of the French decimal week to the standard week is calculated as:

$$\begin{gathered} \frac{frechdecimalweek}{standardweek}=\frac{10}{7} \\ =1.43 \end{gathered}$$

Thus, the ratio of the French decimal week to the standard week is 1.43.

The number of seconds in French decimal day is,

$10\times 100\times 100=100,000seconds$

So, the duration of 1 second in terms of the day is$\frac{1}{100,000}day$

The number of seconds in a standard day is,

$24\times 60\times 60=86,400seconds$

So, the duration of 1 second in terms of the day is,$\frac{1}{86,400}day$

The ratio of the French decimal second to a standard second is calculated as:

$$\begin{gathered} \frac{Frechdecimalseconds}{s\tan daredseconds}=\frac{86,400}{100,000} \\ =0.864 \end{gathered}$$

Thus, the ratio of the French decimal second to the standard second is 0.864 .