Operations with Scientific Notation - Pre Algebra

1. What is $(2 \times 10^3)(4 \times 10^5)$?

   $8 \times 10^8$. Multiply $2 \cdot 4$ and add $3 + 5$.

2. What is $(3 \times 10^4) + (2 \times 10^4)$?

   $5 \times 10^4$. The powers match, so add the coefficients.

3. What is $(5 \times 10^4)(3 \times 10^2)$ in scientific notation?

   $1.5 \times 10^7$. The product $15 \times 10^6$ is adjusted to $1.5 \times 10^7$.

4. What is $\frac{8 \times 10^9}{2 \times 10^3}$?

   $4 \times 10^6$. Divide $8 \div 2$ and subtract $9 - 3$.

5. What is $(2 \times 10^{-3})(3 \times 10^{-4})$?

   $6 \times 10^{-7}$. Multiply $2 \cdot 3$ and add $-3 + (-4)$.

6. How do you multiply two numbers in scientific notation?

   Multiply the coefficients and add the exponents of $10$, then adjust so the coefficient is at least $1$ and less than $10$.

7. How do you divide two numbers in scientific notation?

   Divide the coefficients and subtract the exponents of $10$, then adjust the coefficient if needed.

8. What is $(4 \times 10^3) + (5 \times 10^2)$ in scientific notation?

   $4.5 \times 10^3$. Rewrite $5 \times 10^2$ as $0.5 \times 10^3$, then add.

9. How many times greater is $6 \times 10^8$ than $2 \times 10^5$?

   $3 \times 10^3$ (or $3000$) times. Divide: $\frac{6}{2} = 3$ and $10^{8-5} = 10^3$.

10. What is $(6.0 \times 10^5) - (2.5 \times 10^5)$?

    $3.5 \times 10^5$. The powers match, so subtract the coefficients.

11. What is $\frac{3 \times 10^5}{6 \times 10^2}$ in scientific notation?

    $5 \times 10^2$. The quotient $0.5 \times 10^3$ is adjusted to $5 \times 10^2$.

12. What must be true before you add or subtract two numbers in scientific notation by combining coefficients?

    The powers of $10$ must be the same. Rewrite one number if needed, then add or subtract the coefficients.

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