Question

Drag each place value name to the correct location in Part A. Drag each digit to the correct location on the number in Part B. Each digit can be used more than once, but not all place value names or digits will be used.
Maria rounded all of these numbers to the same place value and found the same rounded value for each. The place value she rounded to was the farthest possible place to the right that would give her the same rounded value for each number.

12.516 13.329
13.478 12.823
In Part A, identify the place value that Maria rounded all of the numbers to. Drag the name of the place value to the box.

In Part B, drag digits to show the rounded value of the numbers. Put one digit in each place, and do not leave any places blank.

Answer 1

To determine the farthest possible place to the right that Maria could have rounded all the numbers to while achieving the same rounded value, let's analyze the numbers provided:

1. **12.516** rounds to **12.5** if rounding to the tenths place.
2. **13.329** rounds to **13.3** if rounding to the tenths place.
3. **13.478** rounds to **13.5** if rounding to the tenths place.
4. **12.823** rounds to **12.8** if rounding to the tenths place.

However, we can see that rounding each number to the tenths gives different rounded values. So, we check the hundredths place as well:

- **12.516** rounds to **12.52** when rounding to the hundredths place.
- **13.329** rounds to **13.33** when rounding to the hundredths place.
- **13.478** rounds to **13.48** when rounding to the hundredths place.
- **12.823** rounds to **12.82** when rounding to the hundredths place.

Again, different rounded values occur.

Now let's round them to the thousandths place to see if they will provide the same value:

1. **12.516** remains **12.516**
2. **13.329** remains **13.329**
3. **13.478** remains **13.478**
4. **12.823** remains **12.823**

Since rounding to the thousandths does not provide the same value either, we will check the tenths and find if any rounding discrepancies exist :

Here are the rounded values again for clarity at tenths:
- **12.516** rounds to **12.5**
- **13.329** rounds to **13.3**
- **13.478** rounds to **13.5**
- **12.823** rounds to **12.8**

The highest rounding point giving distinctive rounded values is **thousandths place** which do not produce the same results.

Revisit rounding to tenths, here **12.516**, **12.823**, and so cannot match the rounding point of **13.329 & 13.478** since their tenths place provide significant changes.

None produced the same arbitrary round to hundredths or thousandths.

Upon concluding, the only number consistent smooth is selecting the **tenths place**.

In Part A, place the following:
- **Tenths**

In Part B:
- 12.5 (for 12.516)
- 13.3 (for 13.329)
- 13.5 (for 13.478)
- 12.8 (for 12.823)

So, the values after rounding would be:
- **Digits in tenths**:
12.5
13.3
13.5
12.8

Thus, rounded values confirm the tenths as isolated unique rounded designation.

Please let me know if you need any further assistance!