Question

Put the numbers in order from least to greatest.

Answer 1

Answer:

$0.5\times{10}^{-5}$,

0.00025,

$3.5\times{10}^{-4}$,

$1.45 \times {10}^{-3}$,

$25.4 \times {10}^{ - 4}$,

0.025,

$1.25\times {10}^{-1}$,

$0.025 \times10$

Step-by-step explanation:

We can do it this way.

First, let us clear off the powers by multipying each number by

${10}^{5}$

This implies that,

$1.25 \times {10}^{ - 1} = 1.25 \times {10}^{ - 1} \times {10}^{5}$

$\implies \: 1.25 \times {10}^{ - 1} = 125 \times {10}^{ - 2} \times {10}^{ - 1} \times {10}^{5}$

$\implies \: 1.25 \times {10}^{ - 1} =125 \times {10}^{( - 2 - 1 + 5)}$

$\implies \: 1.25 \times {10}^{ - 1} =125 \times {10}^{2}= 125 \times 100 = 12500$

$0.00025 = 25 \times {10}^{ - 5} \times {10}^{5}$

$\implies0.00025 = 25 \times {10}^{ - 5 + 5} = 25$

$0.025 = 25 \times {10}^{ - 3}=25 \times{10}^{ - 3}\times {10}^{5}$

$\implies0.025 = 25 \times {10}^{ - 3}=25 \times{10}^{ - 3 + 5}$

$\implies0.025 = 25 \times {10}^{ - 3}=25 \times{10}^{2} = 25 \times 100 = 2500$

$0.025 \times 10=25 \times {10}^{ - 3} \times10 \times {10}^{5}$

$\implies0.025 \times10=25\times{10}^{(- 3 + 1 + 5)}=25\times{10}^{3}$

$\implies0.025\times10=25\times1000 = 25000$

$0.5\times {10}^{-5}=0.5\times {10}^{ - 5} \times {10}^{5}$

$0.5\times{10}^{-5}=0.5\times {10}^{(- 5+5)}=0.5$

$1.45 \times {10}^{-3} = 145 \times {10}^{ - 2} \times {10}^{ - 3} \times {10}^{5}$

$\implies1.45 \times {10}^{-3} = 145$

$25.4 \times {10}^{ - 4} = 254 \times {10}^{-1} \times {10}^{ - 4} \times {10}^{5}$

$\implies25.4 \times {10}^ {-4} = 254$

$3.5 \times{10}^{-4}=35 \times {10}^{-1} \times {10}^{ - 4} \times {10}^{5}$

$\implies3.5 \times{10}^{-4}=35$

Arranging in order from the smallest, we have;

0.5,25,35,145,254,2500,12500,25000

Hence,

$0.5\times{10}^{-5}$,

0.00025,

$3.5\times{10}^{-4}$,

$1.45 \times {10}^{-3}$,

$25.4 \times {10}^{ - 4}$,

0.025,

$1.25\times {10}^{-1}$,

$0.025 \times10$