Percentages At or Above 100 Percent

A percent is just a ratio to 100, so there is nothing stopping it from passing 100 once you're comparing two different amounts instead of splitting one whole into parts. If a number is 250 percent of another, that means for every 100 units the second number has, the first has 250 — in other words, the first is two and a half times the size of the second. Nothing is being carved up into pieces that must stay under one whole; you're just scaling.

The key move is converting the percent into a multiplier. 'x percent of a number' always means multiply by x/100 — no addition involved. But 'a p percent increase' means the new amount is the original plus p percent more of it, so the multiplier becomes 1 + p/100. A channel with 4800 subscribers that grows by 175 percent ends up with 4800 times (1 + 175/100) = 4800 times 2.75 = 13,200 subscribers, not 4800 times 1.75.

This distinction — 'percent of' versus 'percent increase' — is the same skill tested across ratio and growth problems in this unit: scatterplot trend lines, margin of error language, and repeated percent change all hinge on correctly identifying the multiplier before you compute. Mixing up the two phrasings is the single most common way these problems go wrong.