L2 · The value of each digit in a number

Learning goal

“I can find the value of any digit in a number to 100,000 — including a zero — and write a number in expanded form.”

Value of a digit — what a digit is worth in a number: the 4 in 47,306 is worth 40,000.

Expanded form — a number written as the sum of the values of its digits: 47,306 = 40,000 + 7,000 + 300 + 6.

Placeholder — a job the digit 0 does: in 47,306 the 0 holds the tens place so the other digits keep their places. It adds nothing, but the number would change without it.

Worked example

Find the value of each digit in 47,306. Step 1 (place by place): 4 -> ten-thousands -> 40,000. 7 -> thousands -> 7,000. 3 -> hundreds -> 300. 0 -> tens -> 0. 6 -> ones -> 6. Step 2 (expanded form): 47,306 = 40,000 + 7,000 + 300 + 6. The 0 adds no addend — but cross it out and the number collapses to 4,736, a different number. Zero is a placeholder: it holds the tens place. Step 3 (check): 40,000 + 7,000 + 300 + 6 = 47,306.

Check yourself — explain it

The 0 in 47,306 has value 0, but it still matters because...

Paired problem — example still visible

What is the value of the digit 9 in 29,058? -> 9,000 (thousands place: 9 x 1,000)

Faded completion — last step is yours

"In 51,240, the 1 is in the thousands place, so its value is 1 x 1,000 = ___" -> 1,000

Ready to practise?

10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.

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