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}}
=