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

1 answer

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 \(10^{4}\).