Write numbers that satisfy specific conditions related to their range and the placement of certain digits.

Here are the solutions for , Question 3:

3. Write.

• a) A number between 4760 and 4778, with 9 in the ones place. The numbers in this range are $4761, 4762, \dots, 4777$. The only number in this range that has 9 in the ones place is 4769.

  $$\boxed{\text{4769}}$$

• b) Numbers greater than 5615 but less than 5643, with 4 in the ones place. The numbers in this range are $5616, 5617, \dots, 5642$. The numbers in this range that have 4 in the ones place are 5624 and 5634.

  $$\boxed{\text{5624 (or 5634)}}$$

• c) Numbers greater than 3309 but less than 3330, with 5 in the ones place. The numbers in this range are $3310, 3311, \dots, 3329$. The numbers in this range that have 5 in the ones place are 3315 and 3325.

  $$\boxed{\text{3315 (or 3325)}}$$

• d) The number closest to 1679, in which the place value of 8 is 800. A place value of 800 means the digit 8 is in the hundreds place. We are looking for a number of the form $18\text{XX}$ that is closest to 1679. The closest number of the form $18\text{XX}$ to 1679 is 1800.

  $$|1800 - 1679| = 121$$ $$\boxed{\text{1800}}$$

• e) The number closest to 2584 in which the place value of 4 is 400. A place value of 400 means the digit 4 is in the hundreds place. We are looking for a number of the form $24\text{XX}$ that is closest to 2584. Let's check numbers in the 2400s: $|2584 - 2499| = 85$ $|2584 - 2484| = 100$ The number 2499 is the closest.

  $$\boxed{\text{2499}}$$