Math CentralQuandaries & Queries


Question from Natalie, a student:

Is 22/7 bigger or smaller than 3.14?

Hi Natalie,

I would put 22/7 in decimal form by dividing 7 into 22. My calculator gives

\[\frac{22}{7} = 3.14285714285714\]

The challenge in comparing this to 3.14 is that I am not sure what you mean by 3.14.

  • 3.14 might be exactly three and fourteen hundredths, that is $3 \large \frac{14}{100}$ which is 3.140000, with the zero repeating.

  • 3.14 might be the result of calculation where you have rounded the result to two decimal places.

  • It might be that 3.14 is the result of a measurement where your measurement tool is only accurate to two decimal places.

In the first case 22/7 is larger than 3.14 but in the second and third cases the best I can say is that 22/7 and 3.14 agree to two decimal places.

I hope this helps,

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