Understanding price and quantity

In a Trade Capture Report <AE>, the LastQty <32> field is denominated in BTC and the LastPx <31> field is denominated in USD.

Code
RAW
8=FIX.4.4|9=236|35=AE|34=17|49=GEMINI|52=20160301-21:38:35.688|56=CLIENT-DC|31=301.42|32=0.02|55=BTCUSD|60=20160301-21:38:35.591|75=20160301|570=N|571=40987|552=1|54=1|37=40979|11=ORD1|453=1|448=CLIENT-OE|447=D|452=11|12=0.120568|13=3|479=USD|58=TAKER|10=085|

HEADER
        8                   BeginString: FIX.4.4
        9                    BodyLength: 236
       34                     MsgSeqNum: 17
       35                       MsgType: TradeCaptureReport (AE)
       49                  SenderCompID: GEMINI
       52                   SendingTime: 20160301-21:38:35.688
       56                  TargetCompID: CLIENT-DC
BODY
       31                        LastPx: 301.42
       32                       LastQty: 0.02
       55                        Symbol: BTCUSD
       60                  TransactTime: 20160301-21:38:35.591
       75                     TradeDate: 20160301
      570            PreviouslyReported: N
      571                 TradeReportID: 40987
      552                       NoSides: count = 1
       11                       ClOrdID: ORD1
       12                    Commission: 0.120568
       13                      CommType: ABSOLUTE (3)
       37                       OrderID: 40979
       54                          Side: BUY (1)
       58                          Text: TAKER
      479                  CommCurrency: USD
      453                    NoPartyIDs: count = 1
      447                 PartyIDSource: PROPRIETARY_CUSTOM_CODE (D)
      448                       PartyID: CLIENT-OE
      452                     PartyRole: ORDER_ORIGINATION_TRADER (11)
TRAILER
       10                      CheckSum: 085