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43 votes
43 votes
Can someone please help me​

Can someone please help me​-example-1
User BigCat
by
2.6k points

1 Answer

13 votes
13 votes

Answer:

1a. 58/99

1b. 53/90

1c. 29/50

Explanation:

let's start with the easiest one

1.(c)

0.58 = 58/100 = 29/50

that is the simplest possible form, as 29 is a prime number and not a factor of 50.

1.(a)

0.585858585858... = 58×0.0101010101010101...

now, we know that 1/"double digit" (like 1/22) mostly produces a repeating pattern with a period length of 2 after the decimal point.

and we find

1/99 = 0.01010101010101...

so, our solution is

58 × 1/99 = 58/99

that is the simplest possible form, as 58 and 99 do not share any factors.

1.(b)

0.5888888888888... = 0.5 + 0.0888888888888... =

= 0.5 + 8×0.01111111111111... = 0.5 + 8×1/10 × 0.1111111111...

we know how to create 0.11111111111... :

1/9 = 0.111111111111111...

so, our solution is

0.5 + 8 × 1/10 × 1/9 = 0.5 + 8/90 = 5/10 + 8/90 =

= 45/90 + 8/90 = 53/90

this is the simplest possible form, as 53 is already a prime number and not a factor of 90.

User Kulan
by
2.8k points
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