My 84 year grandfather has dementia. does that significantly increase my chances of developing dementia?

Depends: Genes can play a role in the development of dementia, but their effects are complicated and patterns of inheritance vary considerably depending on the type.

Somewhat: It does appear that dementia runs in families. However, there are many types of dementia. Some are not heritable.

Research is unclear: Research on dementia is progressing rapidly, but is not yet definitive. There may be a genetic component to Altzheimer's, but dementia in someone 84 years old is not unusual. There are many causes for dementia, and some are specific to individual (carotid artery plaque, multiple medications with interactions, mild strokes without physical symptoms, etc.). I recommend that you don't worry now.

Minute statistical: It slightly increases the statistical chance but most probably you have a long way to go before this would be an issue. There are all sorts of research going on which which should come to fruition when you are a senior citizen. In the meantime continue to lead a healthy life

Depends: If the cause of his dementia is an inheritable issue, then yes. If it's due to age-related or environmentally-related cause, no.

Not necessarily: Presume he has either Alzheimer's, or a mixed vascular dementia. The hereditary varieties occur at an earlier age, and are more likely due to Fronto-temporal dementia. It is very unlikely that you will develop problems like your grandfather, unless you accumulate risk factors that can trigger a dementia. But statistically, about 50% of adults >85 yrs have dementia by then.