Let's break down the statements:
-
For Matthias:
- He performed an operation with 7.6 and ended up moving the decimal point in 7.6 2 places to the left.
- Moving the decimal point 2 places to the left means multiplying the original number by \(10^{-2}\).
- So, Matthias performed the operation: \[ 7.6 \times 10^{-2} = 0.076 \]
- Thus, we can complete the statement: Matthias performed an operation with 7.6 and ended up moving the decimal point in 7.6 2 places to the left, which is the same as multiplying by \(10^{-2}\).
-
For Irene:
- She performed an operation with 83.904 and ended up moving the decimal point in 83.904 4 places to the right.
- Moving the decimal point 4 places to the right means multiplying the original number by \(10^{4}\).
- So, Irene performed the operation: \[ 83.904 \times 10^{4} = 839040 \]
- Thus, we can complete the statement: Irene performed an operation with 83.904 and ended up moving the decimal point in 83.904 4 places to the right, which is the same as multiplying by \(10^{4}\).
In summary:
- Matthias performed an operation with 7.6 that ended up moving the decimal point in 7.6 2 places to the left, multiplying by \(10^{-2}\).
- Irene performed an operation with 83.904 that ended up moving the decimal point in 83.904 4 places to the right, multiplying by \(10^{4}\).