Compare the numbers in each pair, and give the factor by which the numbers differ.
1.) a. 250 million, 5 billion

b. 9.3x10^2, 3.1x10^-2

c. 10^-8, 2x10^-13

Respuesta :

(1)

For 250 million:

we know that

[tex]1 million=10^{6}[/tex]

so, we can write as

[tex]250million=250\times 10^6[/tex]

we can also write as

[tex]250million=2.5\times 10^2\times 10^6[/tex]

[tex]250million=2.5\times 10^8[/tex]

For 5 billion:

we know that

[tex]1 billion=10^{9}[/tex]

so, we can write as

[tex]5billion=5\times 10^9[/tex]

So, 5 billion is greater than 250 million

Differ factor:

[tex]\frac{5billion}{250million} =\frac{5\times 10^9}{2.5\times 10^8}[/tex]

[tex]\frac{5billion}{250million} =20[/tex]

(b)

we can see that

[tex]9.3\times 10^2[/tex]  is greater than [tex]3.1\times 10^{-2}[/tex]

Differ factor:

[tex]\frac{9.3\times 10^2}{3.1\times 10^{-2}} =\frac{9.3}{3.1}\times 10^{2+2}[/tex]

[tex]\frac{9.3\times 10^2}{3.1\times 10^{-2}} =3\times 10^{4}[/tex]

[tex]\frac{9.3\times 10^2}{3.1\times 10^{-2}} =30000[/tex]

(c)

we can see that

[tex]10^{-8}[/tex]  is greater than [tex]2\times 10^{-13}[/tex]

Differ factor:

[tex]\frac{10^{-8}}{2\times 10^{-13}} =\frac{1}{2}\times 10^{-8+13}[/tex]

[tex]\frac{10^{-8}}{2\times 10^{-13}} =\frac{1}{2}\times 10^{5}[/tex]

[tex]\frac{10^{-8}}{2\times 10^{-13}} =0.5\times 10^{5}[/tex]

[tex]\frac{10^{-8}}{2\times 10^{-13}} =50000[/tex]