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Answer :
To solve the problem, we need to find the ratios as requested:
(a) Ratio of the French decimal week to the standard week:
1. A French decimal week consists of 10 days.
2. A standard week consists of 7 days.
3. To find the ratio of the French decimal week to the standard week, divide the number of days in the French week by the number of days in the standard week:
[tex]\[
\text{Ratio of weeks} = \frac{10 \text{ days (French week)}}{7 \text{ days (standard week)}} \approx 1.4286
\][/tex]
(b) Ratio of the French decimal second to the standard second:
1. In the French decimal system, one day is divided into:
- 10 hours.
- Each hour is divided into 100 minutes.
- Each minute is divided into 100 seconds.
2. Therefore, the total number of seconds in a French day is calculated as follows:
[tex]\[
\text{French day (seconds)} = 10 \text{ hours} \times 100 \text{ minutes per hour} \times 100 \text{ seconds per minute} = 100,000 \text{ seconds}
\][/tex]
3. In the standard system, one day is divided into:
- 24 hours.
- Each hour is divided into 60 minutes.
- Each minute is divided into 60 seconds.
4. Therefore, the total number of seconds in a standard day is calculated as follows:
[tex]\[
\text{Standard day (seconds)} = 24 \text{ hours} \times 60 \text{ minutes per hour} \times 60 \text{ seconds per minute} = 86,400 \text{ seconds}
\][/tex]
5. To find the ratio of a French decimal second to a standard second, divide the number of seconds in a French day by the number of seconds in a standard day:
[tex]\[
\text{Ratio of seconds} = \frac{100,000 \text{ seconds (French day)}}{86,400 \text{ seconds (standard day)}} \approx 1.1574
\][/tex]
These are the ratios: approximately 1.43 for the French week to a standard week and approximately 1.16 for a French second to a standard second.
(a) Ratio of the French decimal week to the standard week:
1. A French decimal week consists of 10 days.
2. A standard week consists of 7 days.
3. To find the ratio of the French decimal week to the standard week, divide the number of days in the French week by the number of days in the standard week:
[tex]\[
\text{Ratio of weeks} = \frac{10 \text{ days (French week)}}{7 \text{ days (standard week)}} \approx 1.4286
\][/tex]
(b) Ratio of the French decimal second to the standard second:
1. In the French decimal system, one day is divided into:
- 10 hours.
- Each hour is divided into 100 minutes.
- Each minute is divided into 100 seconds.
2. Therefore, the total number of seconds in a French day is calculated as follows:
[tex]\[
\text{French day (seconds)} = 10 \text{ hours} \times 100 \text{ minutes per hour} \times 100 \text{ seconds per minute} = 100,000 \text{ seconds}
\][/tex]
3. In the standard system, one day is divided into:
- 24 hours.
- Each hour is divided into 60 minutes.
- Each minute is divided into 60 seconds.
4. Therefore, the total number of seconds in a standard day is calculated as follows:
[tex]\[
\text{Standard day (seconds)} = 24 \text{ hours} \times 60 \text{ minutes per hour} \times 60 \text{ seconds per minute} = 86,400 \text{ seconds}
\][/tex]
5. To find the ratio of a French decimal second to a standard second, divide the number of seconds in a French day by the number of seconds in a standard day:
[tex]\[
\text{Ratio of seconds} = \frac{100,000 \text{ seconds (French day)}}{86,400 \text{ seconds (standard day)}} \approx 1.1574
\][/tex]
These are the ratios: approximately 1.43 for the French week to a standard week and approximately 1.16 for a French second to a standard second.
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