How do you convert 0.254 (4 repeating) as a fraction?

Answer 1

#a/b=229/900#

Let #a/b=0.25444444444444" "#first equation

Multiply both sides of the first equation by 100 and the result is

#100a/b=25.444444444444" "#second equation

Multiply both sides of the first equation by 1000 and the result is

#1000a/b=254.44444444444" "#third equation

Subtract second from the third

#1000a/b-100a/b=254.44444444444-25.444444444444#
#900a/b=229#
#a/b=229/900#

God bless....I hope the explanation is useful

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Answer 2

#0.254444.... = (254-25)/900 = 229/900#

There are easy rules to use for converting recurring decimals to fractions: There are 2 types of recurring decimals - those where ALL the digits recur and those where SOME of the digits recur.

#"the digits which recur"/"a 9 for each digit"#
eg 0.777777...... = #7/9#
0.454545..... = #45/99 rArr "this can be simplified to" 5/11"#
5.714714714.... = #5 714/999 rArr 238/333#
#"2."# If only some digits recur:
#"all the digits - the non-recurring digits"/"a 9 for each recurring digit and 0 for each non-recurring digit"#
eg 0.3544444..... = #(354-35)/900 = 319/900#
eg. 0.4565656... = #(456-4)/990 = 452/990= 226/495#
eg 4.62151515... = #4 6215-62/9900 = 4 6153/9900 = 4 2051/3300#
0.254444.... = #(254-25)/900 = 229/900#

These rules are short cuts for algebraic methods, but it is often useful to be able to get to answer immediately.

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Answer 3

To convert the repeating decimal 0.254(4) into a fraction, you can follow these steps:

  1. Let x = 0.254(4)
  2. Multiply x by 10^k, where k is the number of digits in the repeating part. In this case, k = 1 because there is only one repeating digit (4).
  3. Subtract x from 10^k * x to eliminate the repeating part.
  4. Solve for x to find the fraction.

Following these steps:

  1. Let x = 0.254(4)
  2. Multiply x by 10 (since there is one repeating digit): 10x = 2.544(4)
  3. Subtract x from 10x: 10x - x = 2.544(4) - 0.254(4) = 2.54
  4. Solve for x: 10x - x = 9x = 2.54
  5. Divide both sides by 9: x = 2.54 / 9
  6. Simplify if necessary.

So, 0.254(4) as a fraction is 254/900.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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