Question

Verify that 1 = 0.9​

Answer 1

Answer:

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Step-by-step explanation:

It's Possible Because...

If We Round off 0.9 to once decimal place... than we will get 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 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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