Mr Cervantes drove 3156 miles in December and 8099 miles in January select all choices that are good estimates for the total number of miles Mr Cervantes drove for both months by rounding by place value

The total number of miles Mr. Cervantes drove for both months can be estimated by rounding each monthly total to the nearest hundred, thousand, or ten thousand.

Rounded to the nearest hundred:
December: 3200 miles
January: 8100 miles

Rounded to the nearest thousand:
December: 3000 miles
January: 8000 miles

Rounded to the nearest ten thousand:
December: 0 miles
January: 0 miles

So the good estimates for the total number of miles Mr. Cervantes drove for both months are:
- 3200 + 8100 = 11,300 miles (rounded to the nearest hundred)
- 3000 + 8000 = 11,000 miles (rounded to the nearest thousand)

To estimate the total number of miles Mr. Cervantes drove for both months, we can round each given mileage to the nearest thousand and then add them together.

Rounded mileage for December: 3000 miles
Rounded mileage for January: 8000 miles

When we add these rounded values together, we get:

3000 + 8000 = 11000 miles

Therefore, one good estimate for the total number of miles Mr. Cervantes drove for both months would be 11000 miles.

To estimate the total number of miles Mr. Cervantes drove for both months, you can round the individual month distances to the nearest place value and then sum them up. Let's look at the options:

1. 11000 miles: To get this estimate, round both December (3156 miles) and January (8099 miles) to the nearest thousand. The rounded values would be 3000 miles and 8000 miles. Summing them up gives us 3000 + 8000 = 11000 miles.

2. 10000 miles: If we round both December and January to the nearest ten thousand, we get 0 miles for December and 10000 miles for January. Summing them up gives us 0 + 10000 = 10000 miles.

3. 12000 miles: If we round both December and January to the nearest ten, we get 3160 miles for December and 8100 miles for January. Summing them up gives us 3160 + 8100 = 11260 miles. As 11260 miles is closer to 12000 miles than it is to any other option, 12000 miles can be considered as a reasonable estimate.

Based on the provided options, both 11000 miles and 12000 miles are good estimates for the total number of miles Mr. Cervantes drove for both months, rounded by place value.