Question

Which is larger? How do you know?
2.75 x 103 or 4.92 x 102 ?

Answer 1

To compare the two numbers \(2.75 \times 10^3\) and \(4.92 \times 10^2\), it's helpful to express them in a similar format.

1. Convert \(4.92 \times 10^2\) to the same exponent as \(2.75 \times 10^3\):
\[
4.92 \times 10^2 = 4.92 \times 10^2 = 0.492 \times 10^3
\]

2. Now, compare \(2.75 \times 10^3\) and \(0.492 \times 10^3\):
\[
2.75 \times 10^3 > 0.492 \times 10^3
\]

Since \(2.75\) is greater than \(0.492\), we conclude that:
\[
2.75 \times 10^3 \text{ is larger than } 4.92 \times 10^2.
\]

Thus, \(2.75 \times 10^3\) is the larger number.