The document contains several mathematical questions in Persian, covering various topics such as number properties, place values, arithmetic, and number patterns. Let’s address the questions step-by-step based on the uploaded content.

Translation and Solutions

1. Table for Place Value

   • For the number 304,296,007, the place value table will distribute digits into their respective place values from units to billions.

2. Place Value of the Digit 7

   • In the number 304,296,007, the place value of 7 is 7 (units).

3. Digit with the Lowest Place Value

   • The digit with the lowest place value is 7, as it is in the units place.

4. Five-digit Numbers without Repeating Digits

   • Using the digits 1, 4, 5, 7, 0, the largest and smallest five-digit numbers are:
     • Largest: 75410
     • Smallest: 10457
   • Sum: 75410 + 10457 = 85867

5. Number Patterns

   • Sequence 1: 11, 20, 29, ... (increasing by 9)
     • Next numbers: 38, 47, 56, ...
   • Sequence 2: 1, 4, 16, ... (squares of consecutive numbers: 1, 2, 4, ...)
     • Next numbers: 64, 256, 1024, ...

6. Expanded Form of a Number

   • Expanded form of 120,345,009 is:
     100,000,000 + 20,000,000 + 300,000 + 40,000 + 5,000 + 9

7. Find the Seven-digit Number

   • The number where the tens digit is half the thousands digit, and the units digit is three times the tens digit, is ... (Further clarification is needed for other conditions).

8. Filling Blanks

   • Based on equivalent bundles:
     • 10 packs of hundred-thousands = 1,000,000
     • 10 packs of ten-thousands = 100,000, etc.

9. Compare Numbers

   • Example: Compare 123,879 > 76,543, etc.

10. Father’s Age Problem

    • If Hassan’s father is 12 years older than three times Ali’s age, and Ali’s age is 7 years, then:
      Father’s age = 3 × 7 + 12 = 33 years

11. Price of the Bag

    • If Ali gave a 20,000 Rial note and received 5,000 + 10,000 Rials as change, the price of the bag is:
      20,000 - (5,000 + 10,000) = 5,000 Rials

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If you need a detailed table or expanded explanations, let me know.

Related Questions to Explore:

1. How do place values help in number representation?
2. Can you find other patterns in the sequences provided?
3. How would you solve similar problems involving number comparisons?
4. How can you systematically generate numbers with specific conditions?
5. What strategies are best for solving real-world arithmetic problems?

Tip:

When solving place value problems, always start from the leftmost digit for higher place values and align your table carefully to avoid errors.