Subjects algebra

Potensregler Og Standardform 180Cd3

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1. **State the problem:** Fill out the table by converting numbers to whole numbers or decimals and write them in standard form. 2. **Conversions for Oppgave 3:** - $5\ 800\ 000\ 000 = 5.8 \times 10^{9}$ - $9.35 \times 10^{6} = 9\ 350\ 000$ - $0.00024 = 2.4 \times 10^{-4}$ - $7 \times 10^{-6} = 0.000007$ - $\frac{3}{1000} = 0.003 = 3 \times 10^{-3}$ 3. **Oppgave 4a:** Calculate $$4 \times 10^{6} \times 1\ 600\ 000\ 000 \times 10^{-11}$$ Rewrite $1\ 600\ 000\ 000 = 1.6 \times 10^{9}$ $$= 4 \times 10^{6} \times 1.6 \times 10^{9} \times 10^{-11}$$ Combine powers of ten: $$= 4 \times 1.6 \times 10^{6 + 9 - 11} = 6.4 \times 10^{4}$$ Convert to whole number: $$6.4 \times 10^{4} = 64\ 000$$ 4. **Oppgave 4b:** Calculate $$\frac{28\ 000\ 000 \times 10^{5} \times 600\ 000}{0.0003 \times 10^{18}}$$ Rewrite numbers in standard form: $$28\ 000\ 000 = 2.8 \times 10^{7}, \quad 600\ 000 = 6 \times 10^{5}, \quad 0.0003 = 3 \times 10^{-4}$$ Substitute: $$\frac{2.8 \times 10^{7} \times 10^{5} \times 6 \times 10^{5}}{3 \times 10^{-4} \times 10^{18}} = \frac{2.8 \times 6 \times 10^{7+5+5}}{3 \times 10^{-4+18}}$$ Simplify powers: $$= \frac{16.8 \times 10^{17}}{3 \times 10^{14}}$$ Divide coefficients and powers: $$= \frac{16.8}{3} \times 10^{17-14} = 5.6 \times 10^{3}$$ Convert to whole number: $$5.6 \times 10^{3} = 5600$$ 5. **Oppgave 5:** Calculate average soda consumption per person. Total soda: $400\ 000\ 000$ liters Population: $5\ 000\ 000$ Divide: $$\frac{400\ 000\ 000}{5\ 000\ 000} = 80$$ Each person drinks 80 liters per year. **Final answers:** - Oppgave 3: - $5\ 800\ 000\ 000 = 5.8 \times 10^{9}$ - $9.35 \times 10^{6} = 9\ 350\ 000$ - $0.00024 = 2.4 \times 10^{-4}$ - $7 \times 10^{-6} = 0.000007$ - $\frac{3}{1000} = 3 \times 10^{-3}$ - Oppgave 4a: $6.4 \times 10^{4} = 64\ 000$ - Oppgave 4b: $5.6 \times 10^{3} = 5600$ - Oppgave 5: $80$ liters per person per year