#Pure-bloods often claim to be wizards with no Muggle ancestry.

To the strictest believers in it, being pure-blood supposedly means that the wizard has no Muggle ancestry at all. Other wizards are somewhat more lenient with what classifies someone as a pure-blood, so the definition may vary somewhat depending on who’s using the term.

#Realistically, they’re wizards with very little Muggle ancestry.

The “purest” wizards are the ones who can prove they have no Muggle ancestry for the furthest back through the generations. The Black family can trace their ancestry back to the Middle Ages. 

>“The tapestry looked immensely old; it was faded and looked as though Doxys had gnawed it in places. Nevertheless, the golden thread with which it was embroidered still glinted brightly enough to show them a sprawling family tree dating back (as far as Harry could tell) to the Middle Ages. Large words at the very top of the tapestry read

>*The Noble and Most Ancient House of Black*
<br>*‘Toujours pur”*
<br><sub><sup>*- Harry Potter and the Order of the Phoenix, Chapter 6 (The Noble and Most Ancient House of Black)*</sub></sup> 

Ernie says he’s pure-blood since he can trace his ancestry back through nine generations of witches and wizards. 

>“It was a very near miss,’ said Ernie. ‘And in case you’re getting ideas,’ he added hastily, ‘I might tell you that you can trace my family back through nine generations of witches and warlocks and my blood’s as pure as anyone’s, so –” <br><sub><sup>*- Harry Potter and the Chamber of Secrets, Chapter 11 (The Duelling Club)*</sub></sup> 

However, this leaves the possibility that some of his ancestors from ten or more generations back could be Muggle.