Fractions make me Fractious

Number Theory Level 3

1 2 + 1 4 + 1 8 + 1 16 + 1 32 + 1 64 + x = 1 \large \dfrac12+ \dfrac14 + \dfrac18 + \dfrac1{16} + \dfrac1{32} + \dfrac1{64} + x= 1

What is x x as a decimal rounded to 3 significant figures?


The answer is 0.0156.

Finn C by Finn C , 18, USA

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Sam Bealing
Jun 9, 2016

1 2 + 1 4 + 1 8 + 1 16 + 1 32 + 1 64 + 1 64 = 1 2 + 1 4 + 1 8 + 1 16 + 1 32 + 1 32 = ⋯ = 1 \dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{8}+\dfrac{1}{16}+\dfrac{1}{32}+\dfrac{1}{64}+\color{#3D99F6}{\dfrac{1}{64}}=\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{8}+\dfrac{1}{16}+\dfrac{1}{32}+\dfrac{1}{32}= \cdots=1

1 2 + 1 4 + 1 8 + 1 16 + 1 32 + 1 64 = 1 − 1 64 = 63 64 \dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{8}+\dfrac{1}{16}+\dfrac{1}{32}+\dfrac{1}{64}=1-\dfrac{1}{64}=\dfrac{63}{64}

63 64 + x = 1 ⇒ x = 1 64 \dfrac{63}{64}+x=1 \Rightarrow x=\dfrac{1}{64}

1 64 = 0.015625 = 0.0156 ( 3 s f ) \color{#20A900}{\boxed{\boxed{\dfrac{1}{64}=0.015625=0.0156 \: (3sf)}}}

2 Helpful 0 Interesting 0 Brilliant 0 Confused

Moderator note:

Simple standard approach.

Nice solution

Finn C - 5 years ago

Could you add how to put it to 3 significant figures?

Finn C - 5 years ago

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...