Question

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Convert 3.16 repeating to a fraction. Explain your strategy or show steps you used to convert the number.

Answer 1

What is 3.16161616161616161616 as a fraction?

To write 3.16161616161616161616 as a fraction you have to write 3.16161616161616161616 as numerator and put 1 as the denominator. Now you multiply numerator and denominator by 10 as long as you get in numerator the whole number.

3.16161616161616161616 = 3.16161616161616161616/1 = 31.616161616162/10 = 316.16161616162/100 = 3161.6161616162/1000 = 31616.161616162/10000 = 316161.61616162/100000 = 3161616.1616162/1000000 = 31616161.616162/10000000 = 316161616.16162/100000000 = 3161616161.6162/1000000000 = 31616161616.162/10000000000 = 316161616161.62/100000000000 = 3161616161616.2/1000000000000 = 31616161616162/10000000000000

And finally we have:

3.16161616161616161616 as a fraction equals 31616161616162/10000000000000

Answer 2

Explanation:

3.16161616 ... = 313 99 = 3 16 99

Explanation: It appears that you mean 3.16161616 ... , let x = 3.16161616 ... , then 100 x = 316.16161616 ...

Subtracting former from latter we get 99 x = 313 and x = 313 99 = 3 16 99 Hence 3.16161616 ... = 3 16 99