Question

What is another way to write the expression \( p \cdot (10^{-2}) \)?

a) \( (10 \cdot 2) - p \)
b) \( 10 \cdot 2 - p \)
c) \( (10 \cdot 2) \cdot p \)
d) \( (p \cdot 10) - (p \cdot 2) \)

Answer 1

None of the options provided correctly rewrites the expression p · (10^-2). The correct rewrite would be 0.01p, which is not listed among the choices.

Step-by-step explanation:

To rewrite the expression p \cdot (10^{-2}), we need to understand the property of exponents when dealing with powers of 10. The expression 10^{-2} is equivalent to 1 divided by 10 squared, which is 1/100, or 0.01. Therefore, p \cdot (10^{-2}) simplifies to p \cdot 0.01 or simply 0.01p.

Looking at the options provided:
a) (10 \cdot 2) - p (Incorrect: This represents 20 minus p, not p multiplied by 10 to the power of -2.)
b) 10 \cdot 2 - p (Incorrect: This too represents 20 minus p.)
c) (10 \cdot 2) \cdot p (Incorrect: This represents 20 times p, which is not the same as p times 10 to the power of -2.)
d) (p \cdot 10) - (p \cdot 2) (Incorrect: This expression represents p times 10 minus p times 2.)

Therefore, none of the options correctly rewrite the expression p \cdot (10^{-2}).