Question

verify 1=0.9
please help me
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Answer 1

1 = 0.9

Given,

1 = 0.9

To find,

Verify the above statement.

Solution,

The number "0.9999..." can be "expanded" as:

0.9999... = 0.9 + 0.09 + 0.009 + 0.0009 + ...

In other words, each term in this endless summation will have a "9" preceded by some number of zeroes. This may also be written as:

0.999... = 9/10 + (9/10)(1/10)^1 + (9/10)(1/10)^2 + (9/10)(1/10)^3 + ...

That is, this is an infinite geometric series with first term a = 9/10 and common ratio r = 1/10. Since the size of the common ratio r is less than 1, we can use the infinite-sum formula to find the value:

0.999... = (9/10)[1/(1 - 1/10)] = (9/10)(10/9) = 1

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Answer 2

1 = 0.9

Given,

1 = 0.9

To find,

Verify the above statement.

Solution,

The number "0.9999..." can be "expanded" as:

0.9999... = 0.9 + 0.09 + 0.009 + 0.0009 + ...

In other words, each term in an infinite summation will be preceded by a "9" and a certain amount of zeroes. It's also possible to write it as:

0.999... = 9/10 + (9/10)(1/10)^1 + (9/10)(1/10)^2 + (9/10)(1/10)^3 + ...

That is, this is an infinite geometric series with first term a = 9/10 and common ratio r = 1/10. We can use the infinite-sum formula to obtain the value because the common ratio r is less than 1.

0.999... = (9/10)[1/(1 - 1/10)] = (9/10)(10/9) = 1

#SPJ2