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?

Assume that the definition of a "day" remains the same.

Answer :

(a) The ratio of the French decimal week to the standard week is [tex]\( \frac{10}{7} \)[/tex].

(b) The ratio of the French decimal second to the standard second is [tex]\( \frac{5}{3} \)[/tex].

To find the ratios of the French decimal week to the standard week and the French decimal second to the standard second, we'll compare the durations of these units in the French decimal system to those in the standard system.

(a) Ratio of the French decimal week to the standard week:

In the French decimal system:

- One French decimal week consists of 10 days.

In the standard system:

- One standard week consists of 7 days.

So, the ratio of the French decimal week to the standard week is:

[tex]\[ \text{Ratio} = \frac{\text{French decimal week}}{\text{Standard week}} = \frac{10 \text{ days}}{7 \text{ days}} \][/tex]

(b) Ratio of the French decimal second to the standard second:

In the French decimal system:

- One minute consists of 100 seconds.

In the standard system:

- One minute consists of 60 seconds.

So, the ratio of the French decimal second to the standard second is:

[tex]\[ \text{Ratio} = \frac{\text{French decimal second}}{\text{Standard second}} = \frac{100 \text{ seconds}}{60 \text{ seconds}} \][/tex]

Now, let's simplify these ratios:

(a) Ratio of the French decimal week to the standard week:

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

(b) Ratio of the French decimal second to the standard second:

[tex]\[ \frac{100}{60} = \frac{5}{3} \][/tex]

So, the ratios are:

(a) for the French decimal week to the standard week.

(b) [tex]\( \frac{5}{3} \)[/tex] for the French decimal second to the standard second.

Final answer:

Explanation of the ratios of French decimal time to standard time after the French Revolution.

Explanation:

Ratio of French Decimal Week to Standard Week:

1 French decimal week = 10 days, whereas 1 standard week = 7 days. So, the ratio is 10/7.

Ratio of French Decimal Second to Standard Second:

1 French decimal second = 0.01 standard second since 1 hour = 100 French decimal minutes = 100 x 0.01 = 1 standard hour.

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