1. The problem involves expressing decimal numbers as sums of their parts according to place values and converting them into expanded forms. 2. For exercise 4, given the number $4\,018.82$, the expanded form is: $$4 \times 1000 + 0 \times 100 + 1 \times 10 + 8 \times 1 + 8 \times 0.1 + 2 \times 0.01$$ 3. For exercise 5, express the number $4,142.782$ (which means $4142.782$) as: $$4 \times 1000 + 1 \times 100 + 4 \times 10 + 2 \times 1 + 7 \times 0.1 + 8 \times 0.01 + 2 \times 0.001$$ 4. To express decimals like $0.037$: $$0 \times 1 + 0 \times 0.1 + 3 \times 0.01 + 7 \times 0.001$$ 5. For the number $103.0005$: $$1 \times 100 + 0 \times 10 + 3 \times 1 + 0 \times 0.1 + 0 \times 0.01 + 0 \times 0.001 + 5 \times 0.0001$$ 6. Each term is formed by multiplying the digit by its place value. 7. This expands numbers into sums that clearly show the contribution of each digit. Final answers: - $4,018.82 = 4 \times 1000 + 0 \times 100 + 1 \times 10 + 8 \times 1 + 8 \times 0.1 + 2 \times 0.01$ - $4,142.782 = 4 \times 1000 + 1 \times 100 + 4 \times 10 + 2 \times 1 + 7 \times 0.1 + 8 \times 0.01 + 2 \times 0.001$ - $0.037 = 0 \times 1 + 0 \times 0.1 + 3 \times 0.01 + 7 \times 0.001$ - $103.0005 = 1 \times 100 + 0 \times 10 + 3 \times 1 + 0 \times 0.1 + 0 \times 0.01 + 0 \times 0.001 + 5 \times 0.0001$