Question

③ $(2.15\times10^{-5})(1.4\times10^{8})$ ④ $(2\times10^{4})(8.21\times10^{3})$ ⑤ $(3.5\times10^{8})(7.1\times10^{-9})$

Explanation:

Step1: Use multiplication - property of exponents

When multiplying numbers in scientific - notation \(a\times10^{m}\) and \(b\times10^{n}\), we use the rule \((a\times10^{m})(b\times10^{n})=(a\times b)\times10^{m + n}\).

Step2: Solve problem (3)

For \((2.15\times10^{-5})(1.4\times10^{8})\), first multiply the non - exponential parts: \(2.15\times1.4 = 3.01\). Then add the exponents: \(-5 + 8=3\). So the result is \(3.01\times10^{3}\).

Step3: Solve problem (4)

For \((2\times10^{4})(8.21\times10^{3})\), multiply the non - exponential parts: \(2\times8.21 = 16.42\). Add the exponents: \(4+3 = 7\). So the result is \(16.42\times10^{7}=1.642\times10^{8}\) (rewrite in scientific notation since \(16.42 = 1.642\times10^{1}\)).

Step4: Solve problem (5)

For \((3.5\times10^{8})(7.1\times10^{-9})\), multiply the non - exponential parts: \(3.5\times7.1=24.85\). Add the exponents: \(8+( - 9)=-1\). So the result is \(24.85\times10^{-1}=2.485\) (rewrite in scientific notation as \(24.85\times10^{-1}=2.485\times10^{0}\)).

Answer:

(3) \(3.01\times10^{3}\)
(4) \(1.642\times10^{8}\)
(5) \(2.485\)