Give a rough estimate (by rounding off to nearest hundreds) and also a closer estimate (by rounding off to nearest tens) :
`4,89,348 - 48,365`

Answer

To solve the problem of estimating the difference between 489,348 and 48,365 by rounding off to the nearest hundreds and tens, we can follow these steps:

### Step 1: Round off 489,348 to the nearest hundred.
- The last two digits are 48. Since 48 is less than 50, we round down.
- Therefore, 489,348 rounds to **489,300**.

### Step 2: Round off 48,365 to the nearest hundred.
- The last two digits are 65. Since 65 is 50 or more, we round up.
- Therefore, 48,365 rounds to **48,400**.

### Step 3: Subtract the rounded numbers.
- Now, we subtract the rounded numbers:
\[ 489,300 - 48,400 = 440,900 \]

### Rough Estimate Result:
- The rough estimate by rounding off to the nearest hundreds is **440,900**.

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### Step 4: Round off 489,348 to the nearest ten.
- The last digit is 8. Since 8 is 5 or more, we round up.
- Therefore, 489,348 rounds to **489,350**.

### Step 5: Round off 48,365 to the nearest ten.
- The last digit is 5. Since 5 is 5 or more, we round up.
- Therefore, 48,365 rounds to **48,370**.

### Step 6: Subtract the rounded numbers.
- Now, we subtract the rounded numbers:
\[ 489,350 - 48,370 = 440,980 \]

### Closer Estimate Result:
- The closer estimate by rounding off to the nearest tens is **440,980**.

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### Summary of Results:
- Rough Estimate (nearest hundreds): **440,900**
- Closer Estimate (nearest tens): **440,980**

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