Answer:
[tex]0.5\times{10}^{-5}[/tex],
0.00025,
[tex]3.5\times{10}^{-4}[/tex],
[tex]1.45 \times {10}^{-3}[/tex],
[tex]25.4 \times {10}^{ - 4}[/tex],
0.025,
[tex]1.25\times {10}^{-1}[/tex],
[tex]0.025 \times10[/tex]
Step-by-step explanation:
We can do it this way.
First, let us clear off the powers by multipying each number by
[tex] {10}^{5} [/tex]
This implies that,
[tex]1.25 \times {10}^{ - 1} = 1.25 \times {10}^{ - 1} \times {10}^{5} [/tex]
[tex] \implies \: 1.25 \times {10}^{ - 1} = 125 \times {10}^{ - 2} \times {10}^{ - 1} \times {10}^{5} [/tex]
[tex]\implies \: 1.25 \times {10}^{ - 1} =125 \times {10}^{( - 2 - 1 + 5)}[/tex]
[tex]\implies \: 1.25 \times {10}^{ - 1} =125 \times {10}^{2}= 125 \times 100 = 12500[/tex]
[tex]0.00025 = 25 \times {10}^{ - 5} \times {10}^{5} [/tex]
[tex] \implies0.00025 = 25 \times {10}^{ - 5 + 5} = 25 [/tex]
[tex]0.025 = 25 \times {10}^{ - 3}=25 \times{10}^{ - 3}\times {10}^{5} [/tex]
[tex] \implies0.025 = 25 \times {10}^{ - 3}=25 \times{10}^{ - 3 + 5}[/tex]
[tex]\implies0.025 = 25 \times {10}^{ - 3}=25 \times{10}^{2} = 25 \times 100 = 2500[/tex]
[tex]0.025 \times 10=25 \times {10}^{ - 3} \times10 \times {10}^{5}[/tex]
[tex] \implies0.025 \times10=25\times{10}^{(- 3 + 1 + 5)}=25\times{10}^{3}[/tex]
[tex]\implies0.025\times10=25\times1000 = 25000[/tex]
[tex]0.5\times {10}^{-5}=0.5\times {10}^{ - 5} \times {10}^{5} [/tex]
[tex]0.5\times{10}^{-5}=0.5\times {10}^{(- 5+5)}=0.5[/tex]
[tex]1.45 \times {10}^{-3} = 145 \times {10}^{ - 2} \times {10}^{ - 3} \times {10}^{5} [/tex]
[tex] \implies1.45 \times {10}^{-3} = 145[/tex]
[tex]25.4 \times {10}^{ - 4} = 254 \times {10}^{-1} \times {10}^{ - 4} \times {10}^{5} [/tex]
[tex] \implies25.4 \times {10}^ {-4} = 254[/tex]
[tex]3.5 \times{10}^{-4}=35 \times {10}^{-1} \times {10}^{ - 4} \times {10}^{5} [/tex]
[tex] \implies3.5 \times{10}^{-4}=35[/tex]
Arranging in order from the smallest, we have;
0.5,25,35,145,254,2500,12500,25000
Hence,
[tex]0.5\times{10}^{-5}[/tex],
0.00025,
[tex]3.5\times{10}^{-4}[/tex],
[tex]1.45 \times {10}^{-3}[/tex],
[tex]25.4 \times {10}^{ - 4}[/tex],
0.025,
[tex]1.25\times {10}^{-1}[/tex],
[tex]0.025 \times10[/tex]
