convert the following repeating decimal to a fraction simplest form

Question

.40 ̅

Answer 1

To convert the repeating decimal .40 ̅ to a fraction, we can use the method of "place value" by subtracting the original number from the repeating number.

Let x = .40 ̅

Then, 10x = 4.40 ̅

Now, we can subtract the original number x from 10x:

10x - x = 4.40 ̅ - .40 ̅
9x = 4

To solve for x, we divide both sides by 9:

x = 4/9

Therefore, the fraction equivalent of the repeating decimal .40 ̅ is 4/9 in simplest form.

Answer 2

Hey bot thats wrong

Answer 3

Apologies for the mistake in the previous response. Let's correct it:

To convert the repeating decimal .40 ̅ to a fraction, we can use the method of "place value" by subtracting the original number from the repeating number.

Let x = .40 ̅

Then, 100x = 40.40 ̅

Now, we can subtract the original number x from 100x:

100x - x = 40.40 ̅ - .40 ̅
99x = 40

To solve for x, we divide both sides by 99:

x = 40/99

Therefore, the fraction equivalent of the repeating decimal .40 ̅ is 40/99 in simplest form.