Question

Complete the statements Matthias performed an operation with 7.6 and a number he ended up moving the decimal point in 7.62 places to the left Matthias 10 raised to the power of Irene performed an operation with 83.904 in a number She ended up moving the decimal point in 83.9044 places to the right Irene 10 raised to the power of

Answer 1

Let's break down the statements:

1. 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 \(10^{-2}\).*

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 \(10^{4}\)**.