x <- "24.3483 stuff stuff 34.8325 some more stuff"
stringr::str_extract_all(x, "\\b[0-9]{2}\\.[0-9]{4}.*?(?=\\b[0-9]{2}\\.[0-9]{4}|$)")
eCA8LSAiMjQuMzQ4MyBzdHVmZiBzdHVmZiAzNC44MzI1IHNvbWUgbW9yZSBzdHVmZiIKc3RyaW5ncjo6c3RyX2V4dHJhY3RfYWxsKHgsICJcXGJbMC05XXsyfVxcLlswLTldezR9Lio/KD89XFxiWzAtOV17Mn1cXC5bMC05XXs0fXwkKSIpCg==