Estimate the product by estimating each term to :
a. its greatest place b. nearest 10
(i) `458xx512`
(ii) `297xx716`
(iii) `782xx403`
(iv) `726xx501`

Answer

To solve the problem of estimating the product of the given pairs of numbers, we will follow two parts: estimating each term to its greatest place and estimating each term to the nearest ten.

### Part A: Estimating Each Term to Its Greatest Place

1. **For the first pair (458 and 512):**
- **Estimate 458:** The greatest place is the hundreds place. Since 58 is greater than 50, we round up to 500.
- **Estimate 512:** The greatest place is also the hundreds place. Since 12 is less than 50, we keep it as 500.
- **Product:** \(500 \times 500 = 250000\)

2. **For the second pair (297 and 716):**
- **Estimate 297:** The greatest place is the hundreds place. Since 97 is greater than 50, we round up to 300.
- **Estimate 716:** The greatest place is the hundreds place. Since 16 is less than 50, we keep it as 700.
- **Product:** \(300 \times 700 = 210000\)

3. **For the third pair (782 and 403):**
- **Estimate 782:** The greatest place is the hundreds place. Since 82 is greater than 50, we round up to 800.
- **Estimate 403:** The greatest place is the hundreds place. Since 03 is less than 50, we keep it as 400.
- **Product:** \(800 \times 400 = 320000\)

4. **For the fourth pair (726 and 501):**
- **Estimate 726:** The greatest place is the hundreds place. Since 26 is less than 50, we keep it as 700.
- **Estimate 501:** The greatest place is the hundreds place. Since 1 is less than 50, we keep it as 500.
- **Product:** \(700 \times 500 = 350000\)

### Summary of Part A:
- (i) \(250000\)
- (ii) \(210000\)
- (iii) \(320000\)
- (iv) \(350000\)

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### Part B: Estimating Each Term to the Nearest Ten

1. **For the first pair (458 and 512):**
- **Estimate 458:** The last digit is 8 (greater than 5), so we round up to 460.
- **Estimate 512:** The last digit is 2 (less than 5), so we keep it as 510.
- **Product:** \(460 \times 510 = 234600\)

2. **For the second pair (297 and 716):**
- **Estimate 297:** The last digit is 7 (greater than 5), so we round up to 300.
- **Estimate 716:** The last digit is 6 (greater than 5), so we round up to 720.
- **Product:** \(300 \times 720 = 216000\)

3. **For the third pair (782 and 403):**
- **Estimate 782:** The last digit is 2 (less than 5), so we keep it as 780.
- **Estimate 403:** The last digit is 3 (less than 5), so we keep it as 400.
- **Product:** \(780 \times 400 = 312000\)

4. **For the fourth pair (726 and 501):**
- **Estimate 726:** The last digit is 6 (greater than 5), so we round up to 730.
- **Estimate 501:** The last digit is 1 (less than 5), so we keep it as 500.
- **Product:** \(730 \times 500 = 365000\)

### Summary of Part B:
- (i) \(234600\)
- (ii) \(216000\)
- (iii) \(312000\)
- (iv) \(365000\)

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