Expanded Form And Standard Form Notes & Questions | Class 5 Mathematics | Drishti OS

Expanded Form And Standard Form

What you'll learn

To write a number in expanded form as a sum of the place values of its digits.
To convert an expanded form back into standard (numeral) form.
To use expanded form to understand why the digits of a number add up the way they do.

Key concepts

Level 1 — Standard form to expanded form

Verbal: Break the number into what each digit is really worth, then add a "+" between the parts.

Symbolic: 52,634 = 50,000 + 2,000 + 600 + 30 + 4

Level 2 — Expanded form to standard form

Verbal: Add all the parts together; the result is the standard number.

Symbolic: 40,000 + 3,000 + 500 + 20 + 1 = 43,521

Level 3 — Zero digits in expanded form

Rule: If a digit is 0, it contributes 0 and is usually skipped when writing the expanded form (but its place is still "held" in the standard number).

Example: 30,506 = 30,000 + 500 + 6 (tens and thousands... note the ten-thousands and hundreds carry the non-zero parts; the 0s are simply not written as separate terms).

Worked example

Write 78,205 in expanded form

7 → ten-thousands → 70,000
8 → thousands → 8,000
2 → hundreds → 200
0 → tens → 0 (skip)
5 → ones → 5
Answer: 70,000 + 8,000 + 200 + 5

What number is 60,000 + 4,000 + 300 + 20 + 9?

60,000 + 4,000 = 64,000
64,000 + 300 = 64,300
64,300 + 20 = 64,320
64,320 + 9 = 64,329
Answer: 64,329

Common mistakes

Mistake	Why it happens	Fix
Writing the digit instead of its place value (e.g. "7" instead of "70,000")	Forgetting to multiply by the place	Always attach the correct number of zeros for that place
Adding an extra term for a zero digit	Trying to include every digit	Zero-valued places contribute nothing — skip them
Adding the expanded parts in the wrong order	Careless addition	Add largest to smallest, checking the running total

Quick check

Write 93,048 in expanded form.
What number is 20,000 + 5,000 + 400 + 7?
Write 6,00,010 in expanded form.
Stretch: Two numbers have the same expanded-form parts but written in a different order — are they the same number? Why or why not?

Revision tip: Cover the standard number and rebuild it purely from its expanded form to test yourself.

Open the Practice tab for graded questions on Expanded Form And Standard Form.

Expanded Form And Standard Form