Give a rough estimate (by rounding off to nearest hundreds) and also a closer estimate (by rounding off to nearest tens) :
`439 + 334 + 4,317`

Answer

To solve the problem of estimating the sum of `439 + 334 + 4,317`, we will perform two types of rounding: rounding to the nearest hundred for a rough estimate and rounding to the nearest ten for a closer estimate.

### Step 1: Round each number to the nearest hundred

1. **Round 439 to the nearest hundred:**
- The hundreds place is 4 (400).
- The tens place is 3, which is less than 5.
- Therefore, we round down to **400**.

2. **Round 334 to the nearest hundred:**
- The hundreds place is 3 (300).
- The tens place is 3, which is also less than 5.
- Therefore, we round down to **300**.

3. **Round 4,317 to the nearest hundred:**
- The hundreds place is 3 (4,300).
- The tens place is 1, which is less than 5.
- Therefore, we round down to **4,300**.

### Step 2: Add the rounded numbers

Now we add the rounded numbers:
- 400 + 300 + 4,300

Calculating this gives:
- 400 + 300 = 700
- 700 + 4,300 = **5,000**

So, the rough estimate by rounding off to the nearest hundred is **5,000**.

### Step 3: Round each number to the nearest ten

1. **Round 439 to the nearest ten:**
- The tens place is 3 (30).
- The units place is 9, which is 5 or more.
- Therefore, we round up to **440**.

2. **Round 334 to the nearest ten:**
- The tens place is 3 (30).
- The units place is 4, which is less than 5.
- Therefore, we round down to **330**.

3. **Round 4,317 to the nearest ten:**
- The tens place is 1 (10).
- The units place is 7, which is 5 or more.
- Therefore, we round up to **4,320**.

### Step 4: Add the rounded numbers

Now we add the rounded numbers:
- 440 + 330 + 4,320

Calculating this gives:
- 440 + 330 = 770
- 770 + 4,320 = **5,090**

So, the closer estimate by rounding off to the nearest ten is **5,090**.

### Final Answers:
- Rough estimate (nearest hundreds): **5,000**
- Closer estimate (nearest tens): **5,090**

---