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What are the first 5 digits after the decimal point (technically the hexadecimal point...) when the fraction $\frac{2}{7}$ is written in base $16$?

 Jul 28, 2024
 #1
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0

Start with 0.285714....

Multiply by 16:

0.285714×16=4.571424


Multiply 0.571424 by 16:

0.571424×16=9.142784

 

Multiply 0.142784 by 16:

0.142784×16=2.284544

 

Multiply 0.284544 by 16:

0.284544×16=4.552704

 

Multiply 0.552704 by 16:

0.552704×16=8.843264

 

First digit: 4

Second digit: 9

Third digit: 2

Fourth digit: 4

Fifth digit: 8

 

All combined is 49248

 Jul 30, 2024

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