NumbersExpanded form and standard form of numbers
The expanded form of a number writes it as a sum of the place values of its digits. The usual short way of writing the number is its standard form. Moving between the two is one of the first skills of the number chapter in classes 2 to 5, and it is the clearest way to see what each digit is worth.
How to write the expanded form
- Write the place value of each digit, starting from the left.
- Leave out digits that are 0, since their place value is 0.
- Join the place values with plus signs.
- 358 = 300 + 50 + 8
- 4,072 = 4,000 + 70 + 2
- 60,905 = 60,000 + 900 + 5
- 4,68,253 = 4,00,000 + 60,000 + 8,000 + 200 + 50 + 3
- 70,05,409 = 70,00,000 + 5,000 + 400 + 9
- 3,00,00,025 = 3,00,00,000 + 20 + 5
Three ways it may be asked
Text books use three styles for the same idea. Take 5,208.
- As place values: 5,000 + 200 + 8
- As digit times place: 5 × 1000 + 2 × 100 + 0 × 10 + 8 × 1
- In words: 5 thousands + 2 hundreds + 0 tens + 8 ones
In the second and third styles the zero is often written, to show that the tens place is empty. Follow the style of your own book.
From expanded form back to standard form
Add the parts, taking care with missing places. 6,00,000 + 4,000 + 30 + 9 has no ten thousands and no hundreds. Write a zero in each empty place: 6,04,039. The safest way is to draw the place boxes first and drop each part into its box.
Expanded form with decimals
The same rule carries on to the right of the decimal point. 47.36 = 40 + 7 + 0.3 + 0.06, or 4 × 10 + 7 × 1 + 3 × 1/10 + 6 × 1/100.
Expanded form with powers of ten
From class 7 or 8 the same thing is written with powers. 5,208 = 5 × 10³ + 2 × 10² + 0 × 10¹ + 8 × 10⁰. The small raised number counts how many places the digit is from the ones place.
Do not confuse it with "standard form" in science
In higher classes, "standard form" also means scientific notation, such as 3 × 10⁸. In primary classes it simply means the number written normally. The meaning is clear from the chapter you are in.
Common mistakes
- Writing digits instead of values: 4 + 6 + 8 + 2 + 5 + 3 is not the expanded form of 4,68,253. The parts must be 4,00,000 and so on.
- Losing a zero place when going back to standard form: 3,000 + 7 is 3,007, not 37 or 307.
- Miscounting zeros in a large place value. Check by counting the digits after the one you are expanding.
Why learn it
Expanded form is how mental arithmetic works. To add 346 and 253, most people quietly add 300 + 200, 40 + 50 and 6 + 3. To multiply 23 by 7 they do 20 × 7 and 3 × 7. A child who is at ease with expanded form finds these steps natural.
The converter writes the expanded form of any number. Read next: place value and face value.