I keep hearing that inflation is a measure of purchasing power. To me this means that if inflation is say, 3%, then purchasing power declines by 3%. That can' be true, yes?
Inflation is measure of positive change in price level, but increase in price level means loss of purchasing power. Also, yes if inflation is 3% you loose roughly 3% of your purchasing power.
Suppose at time $t=1$ apple costs \$1, you have \$100 on your account so you can purchase 100 apples. Now suppose there is 3% inflation meaning price level increased by 3% from 100 in $t=1$ to 103 in $t=2$. In our economy where there are only apples that means their price had to increase to \$1.03. Now with your \$100 dollars you can only afford approximately 97.1 apples.
During the 70s inflation was over 6%, but that doesn't tell you that on average you'd expect a 6% loss in gas purchasing power,
Actually it would tell you that there was 6% drop in purchasing power for an average person. The thing is that in real economy (as opposed to the apple economy above) there are millions of goods and services. Price level is calculated from average change in prices of representative basket of this goods usually weighted so it reflects spending pattern of a typical person (see for example the eurostat methodology).
But of course there will be 'lucky' people who spend more money on goods for which prices did not increased as quickly, but equally there will be 'suckers' who spend disproportionately on goods where prices rose faster than the average.
However, an average representative individual/household would expect to loose about 6% purchasing power if there is 6% inflation. Of course, based on your personal situation your experience might differ. Also most people are not exactly average my stats professor in undergraduate school used to say that humans have on average one testicle, but for some people the loss of purchasing power will be worse even if for some it might be better.
This being said unless you are on fixed income (e.g. retiree) usually your wage will also increase in time of inflation. If your wage increases by 4% when inflation is 6% then you will only be able to afford 2% less on monthly basis. But any money that you saved in the past will have 6% less value nonetheless.