Question

1. place a < or > in the circle to complete each statement. 3.05×10^6 ○ 8.25×10^4
2. 5.729×10^2 ○ 6.84×10^2
3. 2.5×10^(-2) ○ 7×10^(-3)

Explanation:

Step1: Compare the powers of 10 in 7.

For \(3.05\times10^{6}\) and \(8.25\times 10^{4}\), since \(10^{6}>10^{4}\), then \(3.05\times10^{6}>8.25\times 10^{4}\).

Step2: Compare the coefficients for the same power of 10 in 8.

Both \(5.729\times10^{2}\) and \(6.84\times10^{2}\) have the same power of 10 (\(10^{2}\)). Since \(5.729 < 6.84\), then \(5.729\times10^{2}<6.84\times10^{2}\).

Step3: Compare the powers of 10 in 9.

For \(2.5\times10^{- 2}\) and \(7\times10^{-3}\), since \(10^{-2}=\frac{1}{10^{2}}\) and \(10^{-3}=\frac{1}{10^{3}}\), and \(\frac{1}{10^{2}}>\frac{1}{10^{3}}\), then \(2.5\times10^{-2}>7\times10^{-3}\).

Answer:

1. >
2. <
3. >