Express the number as a ratio of integers. 0.39 = 0.39393939

1 answer:

3 0

◆ NUMBER SYSTEMS ◆

Let 0.393939... = x
Or , x = 0.393939... ---eq.(1)

Multiplying both sides by 100

We get ,
_____ 100x = 39.393939... --- eq.(2)

Subtracting eq.(1) from eq.(2)

We get ,
100x-x = 39.393939... - 0.393939...
_____ 99x = 39

_____ $x = \frac{39}{99} \\ \\ x = \frac{13}{33} \: \: \: \: \: \: \: \: \: \: \: Ans.$

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ou have two parents, four grandparents, eight great-grandparents, and so forth. (a) If all your ancestors were distinct, what wo

Maslowich

Answer:

Part A:

$2^{40}-2\\=1.0995*10^{12} ancestors$

Part B:

Generations Age=25*39=975 years

Part C:

Some ancestors on different branches of the family tree must be the same.
There could not have been 39 generations in my line of ancestry.

Step-by-step explanation:

Given Data:

Two Parents, Four Grand Parents, Eight great Grand Parents.

Generation=39

Solution:

Part A:

From given data Following series is made:

$2+2^2+2^3+.........+2^{39}$

Now, Above series will become:

$2[1+2+2^2+......+2^{38}]$

From geometric Sequence:

$2[\frac{2^{38+1}-1}{2-1} ]$

$2^{40}-2\\=1.0995*10^{12} ancestors$

Part B:

Generations Age=years*Number of generations

Generations Age=25*39=975 years

Part C:

Number of people lived= 10^11

Ancestors= $1.0995*10^{12} ancestors$

$10^{11}$

It means ancestors are not distinct, it means:

Some ancestors on different branches of the family tree must be the same.
There could not have been 39 generations in my line of ancestry.

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