do we have to have the same amount of significant numbers in the values we got by convertion?

No. Your conversion factors may have some lack of precision.

Examples 60sec=1min infinitely precise, a definition.
1.6km= 1mile two sig figures, because the mile to km is a measured figure. 1 mile = 1.609344 kilometers would be to eight figures. So conversions depend on how precise the conversion factor is. Generally, it is wise to make the conversion factors more precise than the data being converted.

I don't know what you mean by convertion, but there may be no more significant figures in an answer than in the least significant number used to obtain the answer.

When performing calculations or conversions, it is not necessary to have the same number of significant figures in the values you obtained. The number of significant figures in the conversion factors can vary depending on the precision of the conversion factor itself.

For example, let's say you are converting 1.6 kilometers to miles. The conversion factor for this conversion is 1 mile = 1.609344 kilometers. This conversion factor is measured to eight significant figures, but you can choose to use only two significant figures when performing the conversion.

So, the result of the conversion would be 1 mile, which has two significant figures. In this case, the number of significant figures in the result is determined by the least precise value used in the conversion, which is 1.6 kilometers.

It is generally recommended to use conversion factors that are more precise than the data being converted. This helps ensure that the final result is not limited by the precision of the conversion factor.

In summary, the number of significant figures in the values obtained through conversion does not need to be the same. The result will have the same number of significant figures as the least precise value used in the conversion.