Mae rounds a number to the thousand place and gets 13000. Eli rounds the same number to the hundred place and gets 12600. what is the greatest number that can be rounded as described?

Let's break down the problem:

- Mae rounds the number to the **thousand** place and gets **13,000**.
- Eli rounds the same number to the **hundred** place and gets **12,600**.

### Step 1: Interpret Mae's rounding
If Mae rounds the number to 13,000, the number before rounding must be between 12,500 and 13,499, because:
- Any number from **12,500 to 13,499** would round to **13,000** when rounded to the nearest thousand.

### Step 2: Interpret Eli's rounding
If Eli rounds the number to 12,600, the number before rounding must be between 12,550 and 12,649, because:
- Any number from **12,550 to 12,649** would round to **12,600** when rounded to the nearest hundred.

### Step 3: Determine the greatest number
Now, the number must satisfy both conditions:
- It must be between 12,500 and 13,499 (from Mae's rounding).
- It must be between 12,550 and 12,649 (from Eli's rounding).

The overlap between these two ranges is from **12,550 to 12,649**.

Thus, the greatest number that satisfies both rounding conditions is **12,649**.

### Summary:
The greatest number that can be rounded as described is **12,649**.

Do you want further details or have any questions?

Here are 5 related questions to explore:
1. What is the smallest number that could work for both rounding conditions?
2. How does rounding differ when rounding to the nearest ten versus nearest hundred?
3. How does rounding to different places (e.g., tens, hundreds, thousands) affect the range of numbers?
4. Can you have a number that rounds to two different results depending on rounding place value?
5. How would you round the number 12,650 to both the thousand and hundred place?

**Tip:** When rounding a number, identify the range within which the number must lie to round to a particular place value.

Mae rounds a number to the thousand place and gets 13000. Eli rounds the same number to the hundred place and gets 12600. What is the greatest number that can be rounded as described?

Explore how to find the greatest number that rounds to 13000 to the nearest thousand and 12600 to the nearest hundred. This problem demonstrates key concepts of rounding and place value, suitable for students in Grades 4-6.

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