A pip is a tiny portion of the quote currency in any currency pair. It’s 1/10.000 of one unit of the quote currency in non-yen-pairs. And it’s 1/100 of one unit of the quote currency in yen-pairs.
Trading one unit of a currency pair would be a waste of time, because even a price move of several hundred pips would not amount to much, when one pip is such a tiny value. That’s why we trade in
position sizes that are larger than one unit. The school lesson was simply illustrating these facts.
You don’t need to do calculations like the ones in the school lesson in order to construct a trade, but you should know at least approximately the value of one pip in the currency pair and in the lot size you are planning to trade.
Example: If you trade in whole numbers of micro-lots, and you are considering a trade in USD/JPY, you should know that one pip is worth $0.09 per micro-lot. (The easiest way to get that 9¢ pip-value is to use the Pip Value Calculator, here on this site.)
So (continuing this example), if USD/JPY moves 50 pips in your desired direction, a one-micro-lot position will earn 50 x $0.09 = $4.50
In a two-micro-lot position, that same 50-pip move would earn 50 x 2 x $0.09 = $9.00
You are absolutely correct about the ten thousandths, hundred thousandths, etc.
Recall the definition of a pip. Let’s continue with yen-pips as our example. The definition is 1/100 of one yen. Therefore, in a price like USD/JPY = 110.21 (using today’s actual price), we note that the last digit is 1/100 of a yen – which is the definition of one pip (in a yen-pair).
Similarly, in a price like GBP/USD = 1.3072, the last digit is 1/10,000 of a dollar – which is the definition of one pip (in a pair in which USD is the quote currency).
So, when we talk about pips in single units of currency in yen-pairs, we are talking about hundredths of a yen. And when we talk about pips in single units of currency in non-yen-pairs, we are talking about ten thousandths of a unit of whatever the quote currency is.
This is a good place to expound a little on base currencies and quote currencies.
In all EUR-pairs, the EUR is always the base currency. In all JPY-pairs (as we have said several times), the JPY is always the quote currency. All other currencies (USD, GBP, CAD, etc.) can be either base currencies or quote currencies, depending on what they are paired with, according to a specific hierarchy, as follows:
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In all EUR-pairs, the EUR is always the base currency.
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In all GBP-pairs, except EUR/GBP, the GBP is always the base currency.
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In all AUD-pairs, except EUR/AUD, and GBP/AUD, the AUD is always the base currency.
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In all NZD-pairs, except EUR/NZD, GBP/NZD, and AUD/NZD, the NZD is always the base currency.
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In all USD-pairs, except EUR/USD, GBP/USD, AUD/USD, and NZD/USD, the USD is always the base currency.
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— and so forth, down through the minor and exotic currencies, until we come to the JPY —
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In all JPY-pairs, regardless of what the JPY is paired with, the JPY is never the base currency.
One final note: In the school lesson (which started this conversation), and in all of the discussion in this thread so far, prices have been quoted in five digits. In these quotes, the last digit on the right represents whole pips. Six-digit quotes are now the standard (example: EUR/USD = 1.11315). In 6-digit quotes, the last digit represents 1/10 of a pip. Newbies and veterans, alike, have to be careful not to confuse pips with tenths of pips.