How do you convert 1.37 (7 being repeated) to a fraction?

Answer 1

#62/45#

We first let 1.37 (7 being repeated) be #x#.
Since #x# is recurring in 1 decimal places, we multiply it by #10^1#.
#10x = 13.77#

We then deduct them.

#10x - x = 13.77 - 1.37#
#9x = 12.4#
Lastly, we divide both sides by 9 to get #x# as a fraction.
#x = 12.4/9#
#= 124/90#
#= 62/45#
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Answer 2
Let #x=1.377777777....#, then
#10x=13.77777777...# and #100x=137.777777777---#

Removing the second equation from the third gives us

#90x=124#
#x=124/90=62/45#
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Answer 3

x=45/62

1.37 x=1.37 10x=13.7 100x=137.7 100x-10x=137.7-13.7 90x=124 x=124/90 x=45/62

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Answer 4

To convert 1.37(repeating) to a fraction, you can use the formula for repeating decimals: ( x = a.\overline{b} ), where ( x ) is the repeating decimal, ( a ) is the non-repeating part, and ( b ) is the repeating part. In this case, ( a = 1 ) and ( b = 37 ). To convert it to a fraction, subtract the non-repeating part from the whole number, then divide by the repeating part.

So, ( x = 1 + 0.37\overline{37} )

( x - 1 = 0.37\overline{37} )

Multiply both sides by 100 to eliminate the decimal:

( 100x - 100 = 37.\overline{37} )

( 100x = 37.\overline{37} + 100 )

Now, subtract the original equation from the new one to eliminate the repeating part:

( 100x - x = 37.\overline{37} + 100 - (1 + 0.37\overline{37}) )

( 99x = 37 )

( x = \frac{37}{99} )

So, ( 1.37\overline{37} = \frac{37}{99} ).

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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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