To answer the question of which addition problems require annexing zeros to align the place values, we need to examine each problem and determine if the place values of the digits need to be aligned by adding zeros. Here's a detailed, step-by-step analysis of each problem:
1. [tex]$4 + 1.23 + 45.62$[/tex]
- [tex]$4$[/tex] has no decimal part.
- [tex]$1.23$[/tex] has two decimal places.
- [tex]$45.62$[/tex] has two decimal places.
- To align place values, we need to convert [tex]$4$[/tex] to [tex]$4.00$[/tex].
- This problem requires annexing zeros.
2. [tex]$0.09 + 12$[/tex]
- [tex]$0.09$[/tex] has two decimal places.
- [tex]$12$[/tex] has no decimal part.
- To align place values, we need to convert [tex]$12$[/tex] to [tex]$12.00$[/tex].
- This problem requires annexing zeros.
3. [tex]$0.11 + 12.11$[/tex]
- [tex]$0.11$[/tex] has two decimal places.
- [tex]$12.11$[/tex] has two decimal places.
- Both numbers already have the same number of decimal places.
- This problem does not require annexing zeros.
4. [tex]$19.9 + 0.6$[/tex]
- [tex]$19.9$[/tex] has one decimal place.
- [tex]$0.6$[/tex] has one decimal place.
- Both numbers already have the same number of decimal places.
- This problem does not require annexing zeros.
5. [tex]$8.3 + 2 + 6.01$[/tex]
- [tex]$8.3$[/tex] has one decimal place.
- [tex]$2$[/tex] has no decimal part.
- [tex]$6.01$[/tex] has two decimal places.
- To align place values, we need to convert [tex]$2$[/tex] to [tex]$2.00$[/tex] and [tex]$8.3$[/tex] to [tex]$8.30$[/tex].
- This problem requires annexing zeros.
Thus, the addition problems that require annexing zeros to align place values in the addends are:
1. [tex]$4 + 1.23 + 45.62$[/tex]
2. [tex]$0.09 + 12$[/tex]
5. [tex]$8.3 + 2 + 6.01$[/tex]
Therefore, the problems requiring annexing zeros are problems 1, 2, and 5.
