Note: Enter your answer and show all the steps that you use to solve this problem in the space provided. Evaluate the following expressions: 11 0 11 2 11 2 Are the answers in parts a and b the same? Explain why or why not.

Answer 1

There are two expressions given, namely 110112 and 112112.

To evaluate these expressions, we can use the place value chart.

For the first expression:

| | | | | | | | | | | |
|-|-|-|-|-|-|-|-|-|-|-|
|1|1|0|1|1|2| | | | | |

Starting from the rightmost digit, we have:

2 ones = 2

1 twos = 2

1 eights = 8

1 sixteens = 16

1 sixty-fours = 64

Total value = 2 + 2 + 8 + 16 + 64 = 92

Therefore, 110112 = 92.

For the second expression:

| | | | | | | | | | | |
|-|-|-|-|-|-|-|-|-|-|-|
|1|1|2|1|1|2| | | | | |

Starting from the rightmost digit, we have:

2 ones = 2

1 twos = 2

2 eights = 16

1 sixteens = 16

1 sixty-fours = 64

Total value = 2 + 2 + 16 + 16 + 64 = 100

Therefore, 112112 = 100.

The answers in parts a and b are not the same.

110112 = 92

112112 = 100

This is because the two expressions have different digits in the fourth and fifth place, which represent different place values. The fourth digit in 110112 is a 1, while the fourth digit in 112112 is a 2. This means that 110112 represents a smaller number than 112112, since it has a smaller contribution from the fourth digit. Similarly, the fifth digit in 110112 is a 1, while the fifth digit in 112112 is a 2. This means that 110112 represents a smaller number than 112112, since it has a smaller contribution from the fifth digit.