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.
There are two expressions given, namely 110112 and 112112.
To evaluate these expressions, we can use the place value chart.
For the first expression:
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|-|-|-|-|-|-|-|-|-|-|-|
|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.
To evaluate the expression 11 + 0 + 11 / 2, follow the steps:
Step 1: Start with the first operation in the expression, addition:
11 + 0 = 11
Step 2: Move to the next operation in the expression, which is division:
11 / 2 = 5.5
So, the value of the expression 11 + 0 + 11 / 2 is 11 + 5.5 = 16.5.
Now let's evaluate the expression 11 + (0 * 11) / 2.
Step 1: Start with the first operation in the expression, multiplication:
0 * 11 = 0
Step 2: Next, perform the division operation:
0 / 2 = 0
Step 3: Finally, perform the addition:
11 + 0 = 11
Therefore, the value of the expression 11 + (0 * 11) / 2 is 11.
Comparing the two expressions, we find that the result of the first expression is 16.5, while the result of the second expression is 11. Therefore, the answers in parts a and b are not the same because the operations and order of operations performed in the expressions are different.