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 numbers in scientific - notation

For \(3.05\times10^{6}\) and \(8.25\times10^{4}\), since the exponent of \(10\) in \(3.05\times10^{6}\) (\(6\)) is greater than the exponent of \(10\) in \(8.25\times10^{4}\) (\(4\)), \(3.05\times10^{6}>8.25\times10^{4}\).

Step2: Compare second - pair

For \(5.729\times10^{2}\) and \(6.84\times10^{2}\), since the exponents of \(10\) are the same (\(2\)), we compare the coefficients. \(5.729 < 6.84\), so \(5.729\times10^{2}<6.84\times10^{2}\).

Step3: Compare third - pair

For \(2.5\times10^{- 2}\) and \(7\times10^{-3}\), rewrite \(2.5\times10^{-2}=25\times10^{-3}\). Since \(25>7\), \(2.5\times10^{-2}>7\times10^{-3}\).

Answer:

1. \(>\)
2. \(<\)
3. \(>\)