Question

Tamara estimates her horse will eat about 5,000 pounds of hay each year. How is 5,000 written using exponents?

a. 5 x 10^1
b. 5 x 10^2
c. 5 x 10^3
d. 5 x 10^4

Answer 1

5,000 written using exponents is 5 x 10^3. This is represented by identifying the most significant digit and the power of 10 needed to reach the thousand place, which in this case is three.

Step-by-step explanation:

The question asks for the number 5,000 to be written using exponents. To express a number using exponential notation, we find a base (usually 10 for simplicity) and an exponent that reflects how many times we use the base in multiplication to reach the original number.

Here is how we do it step-by-step for 5,000:

1. Identify the most significant digit in 5,000, which is 5.
2. Count how many times we need to multiply 10 to reach the thousand place. In this case, it's three times (10 x 10 x 10).
3. Write the number as 5 times 10 raised to the power of the number of times we multiplied 10, which gives us 5 x 10^3.

Therefore, the correct answer is c. 5 x 10^3.