Scientific Notation - Pre Algebra

1. What is $0.0032$ in scientific notation?

   $3.2 \times 10^{-3}$. Move the decimal point $3$ places right, so the exponent is negative.

2. What form does a number in scientific notation take?

   $a \times 10^n$, where $1 \le a < 10$ and $n$ is an integer.

3. What is $6.1 \times 10^5$ in standard form?

   $610{,}000$. Move the decimal point $5$ places right.

4. What is $7 \times 10^{-4}$ in standard form?

   $0.0007$. Move the decimal point $4$ places left.

5. Which is greater, $3 \times 10^{-2}$ or $9 \times 10^{-3}$?

   $3 \times 10^{-2}$. It equals $0.03$, while $9 \times 10^{-3} = 0.009$.

6. What is $8{,}000{,}000$ in scientific notation?

   $8 \times 10^6$. Move the decimal point $6$ places left.

7. What is $1.03 \times 10^2$ in standard form?

   $103$. Move the decimal point $2$ places right.

8. What is $0.000056$ in scientific notation?

   $5.6 \times 10^{-5}$. Move the decimal point $5$ places right.

9. In scientific notation, what does a negative exponent tell you about a positive number?

   The number is between $0$ and $1$.

10. Which is greater, $5.2 \times 10^7$ or $2.5 \times 10^8$?

    $2.5 \times 10^8$. With proper coefficients, the larger power of $10$ gives the larger number.

11. Why is $12 \times 10^3$ not in scientific notation, and what is the correct form?

    The coefficient $12$ is not less than $10$. The correct form is $1.2 \times 10^4$.

12. What is $45{,}000$ in scientific notation?

    $4.5 \times 10^4$. Move the decimal point $4$ places left.

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