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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

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MrRoyal

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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