Drag to sort

Rational numbers are either terminating or repeating decimals.

stop_circle Terminating
all_inclusive Repeating
check_circle All sorted!

Tap to select

Tap the digits that form the first repeating block.

0.
...

check_circle Pattern found! Let x = 0.{{problemData.repetend}}...

Slide to align

Multiply x so the repeating decimal parts match exactly.

{{step3Multiplier}}x
=
{{step3ShiftedInt}}
.{{step3ShiftedDec}}
1x
=
0
.{{step3OrigDec}}
×1 ×10 ×100 ×1000

Tap to solve

Subtract the equations to eliminate the repeating part.

{{problemData.multiplier}}x = {{problemData.repetendVal}} .{{problemData.repetend}}{{problemData.repetend}}...
- 1x = 0 .{{problemData.repetend}}{{problemData.repetend}}...
{{ step4LeftVal !== null ? step4LeftVal : '' }}
x =
{{ step4RightVal !== null ? step4RightVal : '' }}
🎉

You did it!

You converted the repeating decimal to a fraction!

0.{{problemData.repetend}} =