High School

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?
(b) The French decimal second to the standard second?

Answer :

Answer:

[tex](a)\ Ratio = 1.43[/tex]

[tex](b)\ Ratio = 0.864[/tex]

Step-by-step explanation:

Given

[tex]French\ Week= 10\ days[/tex]

[tex]French\ days= 10\ hours[/tex]

[tex]French\ hours= 100\ minutes[/tex]

[tex]French\ minutes= 100\ seconds[/tex]

Solving (a): Ratio of french minute to standard week

This is calculated as:

[tex]Ratio = \frac{French\ week}{Standard\ week}[/tex]

[tex]Ratio = \frac{10\ days}{7\ days}[/tex]

[tex]Ratio = \frac{10}{7}[/tex]

[tex]Ratio = 1.43[/tex]

Solving (b): Ratio of french second to standard second

This is calculated as:

[tex]Ratio = \frac{French\ second}{Standard\ second}[/tex]

Convert french days to seconds

[tex]French\ days= 10\ hours[/tex]

[tex]French\ days = 10hr * 100mins/hr * 100secs/min[/tex]

[tex]French\ days = 10 * 100 * 100secs[/tex]

[tex]French\ days = 100000\ secs[/tex]

This gives:

[tex]French\ second = \frac{1}{100000}day[/tex]

For standard day, we have:

[tex]Standard\ second = \frac{1}{86400}day[/tex]

So, we have:

[tex]Ratio = \frac{1/100000}{1/86400}[/tex]

Rewrite as:

[tex]Ratio = \frac{1}{100000} \div \frac{1}{86400}[/tex]

[tex]Ratio = \frac{1}{100000} * \frac{86400}{1}[/tex]

[tex]Ratio = \frac{86400}{100000}[/tex]

[tex]Ratio = 0.864[/tex]

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