Is 1.0000... ( 1 with infinite zeros) greater than 1.0? Given that 0.3333... is greater...

Lorena Beard

Lorena Beard

Answered

2022-07-13

Is 1.0000... ( 1 with infinite zeros) greater than 1.0?
Given that 0.3333... is greater than 0.3 and similarly 0.777... is greater than 0.7, does it follow that the sum of 0.33... and 0.77... is greater than sum of 0.3 and 0.7?

Answer & Explanation

Nicolas Calhoun

Nicolas Calhoun

Expert

2022-07-14Added 15 answers

This is clearer to see when using fraction notation:
0. 3 ˙ = 1 3 , 0. 7 ˙ = 7 9 , 0.3 = 3 10 , 0.7 = 7 10
So:
0. 3 ˙ + 0. 7 ˙ = 1 3 + 7 9 = 10 9 = 1. 1 ˙ > 1 0.3 + 0.7 = 3 10 + 7 10 = 10 10 = 1
Not only is it greater, it doesn't actually equal 1.000 , but rather 1.111
Note that I've used dots above the number to repeated decimal expansion, for example: 0. 1 ˙ = 0.111
Michelle Mendoza

Michelle Mendoza

Expert

2022-07-15Added 3 answers

Yes, 0.33 + 0.77 > 0.3 + 0.7
No, 1.000 1.0

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