Before replying your question, some introductory notes should be reminded.
1. Hijab literally means curtain and veil and the thing which comes between two things.[1] Of course as the Qur'an commentators and researchers have said the word "hijab" meaning women's covering is a term that has mostly emerged in modern age and it is in fact a new term. The word that has been used in the past especially in Muslim jurisprudents' tongue was the word "sitr" which means covering.[2]
The necessity of having covering for women before a non-Mahram man is one of the important Islamic issues. In the Holy Qur'an in order for women to develop and uplift spiritually and also in order for the family and society to get purified ,hijab has become an obligatory task for women.[3]
2. There is no doubt that God always knows every thing and there is no hidden and secret thing for Him, but since a human being considers himself/herself in the presence of God while being busy speaking to God, he/she should wear the most proper clothing of his/her in His presence and it is evident that the best covering for a female person is the most complete one; that is, the clothing which shows her chastity and continence; This kind of clothing reflects the best mood of a woman. Only such clothing deserves worshipping. As far as male people are concerned, it should be said that not only performing prayers with a bare body is void and contrasts with the spirit of modesty and respect to the Holy Self of the Lord, but also it is better to perform prayers with the clothing which shows the utmost respect.
In addition, being covered with hijab while performing prayers is :
1. A kind of continuous and daily practice of observing hijab in all obligatory cases
2. performing prayers in people's eyes, public places, and mosques which requires complete hijab and also safety of female figures from looks of other people leads toward spiritual peacefulness of prayer-performer.[4] As concerns the quality and limits of hijab to be observed on the part of women while performing prayers:
The obligatory limits of covering for a woman while performing her prayers is to cover the entire body as well as hairs except for the face (to the extent that is washed in wudu), hands and feet to the wrist and ankle. But in order to ensure that she has observed the obligatory limits she should also cover rounds of her face and lower sides of her wrists ankles to some extent.[5]
Please pay attention to some istifta in this regard:
Covering in Prayers
Question :Being busy with performing her prayer, if a woman finds out that a part of her hairs has been uncovered out of her chador, what is her duty? What about the case where she becomes aware of such a fact after her prayer finishes?
According to all religious authorities – except for Ayatollahs Bahjat and Wahid, if she becomes aware of it amidst her prayer, she should immediately cover her hairs and her prayer is correct provided that covering her hairs does not take long time. If she comes to know the matter after her prayer, it will be correct.
Ayatollahs Bahjat and Wahid: If she becomes aware amidst her prayer, she should immediately cover it and observing compulsory precaution she should finish it and then performs it again and if she becomes aware of it after her prayer, it will be correct.
Performing Prayer with uniform
Q: What is the rule of performing prayer with uniform and scarf (rosary )?
According to all religious authorities, there will be no problem provided that the compulsory extent of covering and conditions of clothes of a prayer performer are observed though wearing chador is easier and better to be covered in prayers.
Covering feet and Chin
Q: Is it compulsory to cover soles while performing prayer?
A: No; according to all religious authorities the answer is negative. It is NOT compulsory to cover foot and soles.
Replying the question that whether it was compulsory to cover the chin completely while observing hijab or performing prayer or it is just compulsory to cover the bottom of the chin and that whether covering the chin is a primary task for covering the face that is compulsory in religion, Grand Ayatollah Khamenei stated that it was obligatory to cover the area at the bottom of the chin not the chin itself because it is a part of the face.
By taking the above-said notes and also by reflecting for a short period of time you can easily come to know that whether your chador provides the compulsory cover needed for prayers or not.

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