Problem Set 5 – Place Value and Expanded FormClass 5 Maths · Chapter 2 Number Work · Problem Set 5 – Maharashtra Board

Summary: Problem Set 5 – Place Value and Expanded Form

The place name tells WHERE a digit sits (units, tens, … ten lakhs). The place value tells HOW MUCH the digit is worth there.

Place value = digit × value of its place. In 24,61,380 the 4 is in the lakhs place, so its place value is 4,00,000.

Writing a number as the sum of the place values of its digits gives its expanded form: 5,07,936 = 5,00,000 + 7,000 + 900 + 30 + 6.

A 0 has place value 0. We may write '+ 0' for it or simply leave it out.

To go back from expanded form to the number, put each digit in its place and write 0 in places that are missing.

Key points to remember

• Place name = name of the place
• Place value = what the digit is worth there
• Same digit, different place → different value
• Place value of 0 is always 0
• Expanded form = sum of place values
• Zeros may be left out of the expanded form
• Missing places become 0 in the number
• Each place is worth 10 times the place on its right

Problem Set 5 – Place Value and Expanded Form – Notes

1. Place names

• In a seven-digit number the places from the right are: units, tens, hundreds, thousands, ten thousands, lakhs, ten lakhs.
• Draw a place table (TL, L, TTh, Th, H, T, U) and write one digit in each box.
• Moving one place to the left makes a digit worth ten times more.

2. Place value

• Multiply the digit by the value of its place.
• In 24,61,380: 2 is in ten lakhs → 20,00,000; 4 is in lakhs → 4,00,000; 6 is in ten thousands → 60,000.
• The digit 5 in 5,000 is worth 5,000, but in 50 it is worth only 50.

3. Expanded form

• Write the place value of every digit and join them with '+'.
• Zeros may be shown as + 0 or left out — both are correct.
• Add the parts back to check that you get the number again.

4. From expanded form back to the number

• Find the place of each part: 40,00,000 is ten lakhs, 6,00,000 is lakhs, 2,000 is thousands…
• Write each digit in its place, and 0 where no part is given.
• 40,00,000 + 6,00,000 + 2,000 + 80 + 1 → 4 6 | 0 2 | 0 8 1 → 46,02,081.

5. The dice number game

• Each player throws a dice and writes the number in one box of a seven-digit table.
• To make a BIG number, put large throws in the high places (ten lakhs, lakhs). Put small throws in the units and tens.
• To make a SMALL number, do the opposite. This game trains you to think about place value.

Formulas at a glance

Key terms

Problem Set 5 – Place Value and Expanded Form – Flashcards

Read the question, answer it in your head, then tap the card to check. 10 cards.

Problem Set 5 – Place Value and Expanded Form – MCQ Quiz

10 questions. Tap an option — you will see at once if it is right and why.

How to study Problem Set 5 – Place Value and Expanded Form

⏱ About 25 minutes

1. Learn (5 min)
   Draw a place table TL, L, TTh, Th, H, T, U and learn the value of each place.
2. Write (15 min)
   Write three numbers in expanded form and turn three expanded forms back into numbers.
3. Practise (5 min)
   Do the 4 'Try it yourself' sums, take the quiz and play 🎮 Play.