Question

Put the numbers in order from least to greatest.

1.25 x 10^-1,
0.00025,
0.025,
0.025 x 10,
0.5 x 10^-5,
1.45 x 10^ -3,
25.4 x 10^ -4,
3.5 x 10 ^ -4

Answer 1

`0.5*{10}^(-5)`,

0.00025,

`3.5*{10}^(-4)`,

`1.45 * {10}^(-3)`,

`25.4 * {10}^( - 4)`,

0.025,

`1.25* {10}^(-1)`,

`0.025 *10`

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 * {10}^( - 1) = 1.25 * {10}^( - 1) * {10}^(5)`

`\implies \: 1.25 * {10}^( - 1) = 125 * {10}^( - 2) * {10}^( - 1) * {10}^(5)`

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

`\implies \: 1.25 * {10}^( - 1) =125 * {10}^(2)= 125 * 100 = 12500`

`0.00025 = 25 * {10}^( - 5) * {10}^(5)`

`\implies0.00025 = 25 * {10}^( - 5 + 5) = 25`

`0.025 = 25 * {10}^( - 3)=25 *{10}^( - 3)* {10}^(5)`

`\implies0.025 = 25 * {10}^( - 3)=25 *{10}^( - 3 + 5)`

`\implies0.025 = 25 * {10}^( - 3)=25 *{10}^(2) = 25 * 100 = 2500`

`0.025 * 10=25 * {10}^( - 3) *10 * {10}^(5)`

`\implies0.025 *10=25*{10}^((- 3 + 1 + 5))=25*{10}^(3)`

`\implies0.025*10=25*1000 = 25000`

`0.5* {10}^(-5)=0.5* {10}^( - 5) * {10}^(5)`

`0.5*{10}^(-5)=0.5* {10}^((- 5+5))=0.5`

`1.45 * {10}^(-3) = 145 * {10}^( - 2) * {10}^( - 3) * {10}^(5)`

`\implies1.45 * {10}^(-3) = 145`

`25.4 * {10}^( - 4) = 254 * {10}^(-1) * {10}^( - 4) * {10}^(5)`

`\implies25.4 * {10}^ {-4} = 254`

`3.5 *{10}^(-4)=35 * {10}^(-1) * {10}^( - 4) * {10}^(5)`

`\implies3.5 *{10}^(-4)=35`

Arranging in order from the smallest, we have;

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

Hence,

`0.5*{10}^(-5)`,

0.00025,

`3.5*{10}^(-4)`,

`1.45 * {10}^(-3)`,

`25.4 * {10}^( - 4)`,

0.025,

`1.25* {10}^(-1)`,

`0.025 *10`