CPM Homework Help : GB8I Problem 1-70

Scientific notation requires that one factor is a power of $10$ and the other factor is a number greater than or equal to $1$ but less than 10. For example, $2.56 × 10^5$ is correctly written in scientific notation, but $25.6 × 10^4$ is not. See the Math Notes box in this lesson for more information. Scientific notation also uses the symbol “ $\times$ ” for multiplication instead of using “·” or parentheses.

None of the numbers below is correctly written in scientific notation. Explain why each one does not meet the criteria for scientific notation, then write it using correct scientific notation.

$62.5 × 10^3$
Hint (a):
Review the Math Notes box in this lesson.
More Help (a):
Is one factor a power of $10$ ?
Is the other factor greater than or equal to $1$ , but less than $10$ ?
Answer (a):
Since $62.5$ is not less than $10$ , rewrite $62.5$ in scientific notation and then simplify as shown in the Math Notes box.
$62.5\times 10^3$
$6.25\times 10^1 \times 10^3$
$6.25 \times 10^4$

$6.57 · 1000$
Hint (b):
There are two problems to fix: A symbol and a factor that is not a power of $10$ .

$0.39 × 10^9$
Answer (c):
$3.9 \times 10^8$