Learn about number work through these example problems with detailed step-by-step solutions.
Example 1: Reading and Writing Large Numbers (Indian System)
Write the number 74,52,981 in words.
Step 1: Read the number by placing commas according to the Indian system (starting from the right: ones, tens, hundreds, thousands, ten thousands, lakhs, ten lakhs, crores). The number is 74,52,981.
Step 2: Read the number in each period (groups of digits separated by commas) from left to right.
- The digits before the first comma (from the left) are 74, which are in the Lakhs period. So, "Seventy-four Lakh".
- The digits between the first and second comma are 52, which are in the Thousands period. So, "fifty-two Thousand".
- The digits after the second comma are 981, which are in the Units period. So, "nine hundred eighty-one".
Step 3: Combine the parts, adding the period names: Seventy-four Lakh fifty-two Thousand nine hundred eighty-one.
Step 4: Therefore, the number 74,52,981 in words is Seventy-four Lakh fifty-two Thousand nine hundred eighty-one.
Example 2: Writing Number in Expanded Form
Write the number 5,93,045 in expanded form.
Step 1: Identify the place value of each digit in the number 5,93,045.
- 5 is in the Lakhs place (1,00,000)
- 9 is in the Ten Thousands place (10,000)
- 3 is in the Thousands place (1,000)
- 0 is in the Hundreds place (100)
- 4 is in the Tens place (10)
- 5 is in the Ones place (1)
Step 3: Write the number as the sum of the products from Step 2.
5,93,045 = 5,00,000 + 90,000 + 3,000 + 0 + 40 + 5
Step 4: Therefore, the expanded form of 5,93,045 is 5,00,000 + 90,000 + 3,000 + 40 + 5. (You can omit the term with 0).
Example 3: Writing Number from Expanded Form
Write the number for the expanded form: 8,00,000 + 50,000 + 7,000 + 200 + 10 + 6.
Step 1: Identify the place value represented by each term in the expanded form.
- 8,00,000 is 8 Lakhs
- 50,000 is 5 Ten Thousands
- 7,000 is 7 Thousands
- 200 is 2 Hundreds
- 10 is 1 Ten
- 6 is 6 Ones
Step 2: Place the digit corresponding to each place value in its correct position. If a place value is missing in the expanded form, put a 0 in that place.
Lakhs: 8
Ten Thousands: 5
Thousands: 7
Hundreds: 2
Tens: 1
Ones: 6
Step 3: Combine the digits to form the number, using commas according to the Indian system.
The digits are 8, 5, 7, 2, 1, 6.
Arranging them from left to right: 857216.
Placing commas: 8,57,216.
Step 4: Therefore, the number for the expanded form 8,00,000 + 50,000 + 7,000 + 200 + 10 + 6 is 8,57,216.
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Related Concepts
Explore these related mathematical concepts to deepen your understanding of number work.
Place Value (Indian System)
Understanding the value of each digit based on its position using the Indian system (ones, tens, hundreds, thousands, lakhs, crores).
International Place Value System
Learning about another system of place value (ones, tens, hundreds, thousands, millions, billions) and how it differs from the Indian system.
Expanded Form
Writing a number as the sum of the values of its digits (e.g., 123 = 100 + 20 + 3).
Face Value and Place Value
Distinguishing between the digit itself (face value) and its value based on its position (place value).