Unit 1 · Topic 11 · Number System & Notation
The number 5,258 has the digit 5 written twice.
Kabir said both 5s were 'worth the same' since they were the same digit.
Anaya said one of them was worth exactly 1000 times more than the other.
Ms. Rao wrote 5,258 on the board and circled both 5s. "These are the same digit. Are they worth the same amount?" Kabir said yes — a 5 is a 5. Anaya disagreed.
"Look at where each one sits," she said. "The first 5 is in the thousands place. The second 5 is in the tens place." She wrote it out: 5 thousands, 2 hundreds, 5 tens, 8 ones.
"So the first 5 is really worth 5,000. The second 5 is really worth 50. That's the digit's PLACE VALUE — what it's actually worth because of where it's sitting."
"But if I just ask 'what digit is that?', the answer for both is simply 5," said Kabir. "That plain answer — just the digit itself, no matter where it sits — is called the FACE VALUE. The face value of both 5s is 5. Always. It never changes."
Ms. Rao gave them a trickier number: 30,503. "Face value of every digit here?" Anaya read them off: 3, 0, 5, 0, 3 — exactly as written, digit by digit. "Now place value of each 3?" Anaya worked through the place columns: the first 3 sits in the ten-thousands place, so its place value is 30,000. The second 3 sits in the ones place, so its place value is just 3.
"Same digit, same face value, wildly different place value," said Kabir, "just because of where each one is standing." "Exactly," said Ms. Rao. "Face value asks 'what digit is written?' Place value asks 'what is this digit actually worth, right here, in this exact spot?' Two completely different questions about the very same mark on the page."
FACE VALUE is simply the digit itself, exactly as written, with no regard to its position. The face value of 5 is always 5, whether it appears in the ones place or the ten-lakhs place.
PLACE VALUE is what a digit is actually worth because of where it sits in the number. It equals the digit multiplied by the value of its place: ones, tens, hundreds, thousands, and so on.
The same digit can appear more than once in a number with the same face value every time, but a completely different place value each time, depending on which column it occupies.
To find a digit's place value, identify which place (ones, tens, hundreds, thousands...) it sits in, then multiply the digit by that place's value (1, 10, 100, 1000...).
Write down any 5-digit number with a repeated digit. State the face value and place value of each occurrence of that digit.
Take the number 47,074 and find the place value of every digit in it, one column at a time.
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