9) It was Saturday on January 1, 2005. Find the day of the week on January 1, 2010. using day codes

To determine the day of the week on January 1, 2010, using day codes, we'll go through the steps methodically:

### Step 1: Calculate the number of years from 2005 to 2010.
From January 1, 2005, to January 1, 2010, is exactly 5 years.

### Step 2: Determine the number of leap years between 2005 and 2010.
Leap years are years divisible by 4. However, years divisible by 100 are not leap years unless they are also divisible by 400.
- 2005: Not a leap year.
- 2006: Not a leap year.
- 2007: Not a leap year.
- 2008: **Leap year**.
- 2009: Not a leap year.

So, there is 1 leap year (2008) between 2005 and 2010.

### Step 3: Calculate the total number of extra days.
Each ordinary year contributes 1 extra day to the day of the week, and a leap year contributes 2 extra days.
- Ordinary years (2005, 2006, 2007, 2009): 4 years × 1 day = 4 days.
- Leap year (2008): 2 days.

Total extra days = 4 days + 2 days = 6 days.

### Step 4: Find the day of the week on January 1, 2010.
Since January 1, 2005, was a Saturday, we add the 6 extra days to Saturday:

- Saturday + 1 day = Sunday.
- Sunday + 1 day = Monday.
- Monday + 1 day = Tuesday.
- Tuesday + 1 day = Wednesday.
- Wednesday + 1 day = Thursday.
- Thursday + 1 day = **Friday**.

### Conclusion:
January 1, 2010, was a **Friday**.

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Would you like more details on how day codes work or have any other questions? Here are 5 related questions you might find interesting:

1. How do day codes work in calculating the day of the week?
2. How can you quickly determine if a year is a leap year?
3. What other methods can be used to find the day of the week for a given date?
4. Can you calculate the day of the week for your birthday in a future year?
5. How does the Gregorian calendar affect the calculation of days of the week?

**Tip:** Remember that leap years are crucial in determining the day of the week over a span of years!

It was Saturday on January 1, 2005. Find the day of the week on January 1, 2010, using day codes.

Find out how to determine the day of the week for January 1, 2010, using day codes. This problem involves calendar calculations, understanding leap year rules, and applying the day code formula. Ideal for students in Grades 6-8.

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