Class 8 Exam > Class 8 Notes > Mathematics Class 8- New NCERT (Ganita Prakash) > Learning Poster: Place Value System
Learning Poster: Place Value System | Mathematics Class 8- New NCERT (Ganita Prakash) PDF Download
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FAQs on Learning Poster: Place Value System - Mathematics Class 8- New NCERT (Ganita Prakash)
| 1. What is the place value system, and why is it important in mathematics? |  |
Ans. The place value system is a method of representing numbers in which the position of each digit determines its value. For example, in the number 345, the digit 3 represents three hundreds, 4 represents four tens, and 5 represents five units. This system is crucial in mathematics because it allows for the clear understanding of the magnitude of numbers, facilitates arithmetic operations, and forms the basis for more complex mathematical concepts.
| 2. How do you determine the place value of a digit in a large number? | |
Ans. To determine the place value of a digit in a large number, you need to identify its position within the number. Starting from the right, the first position is the units place, the second is the tens place, the third is the hundreds place, and so on, increasing by a factor of ten for each subsequent position. For example, in the number 7,852, the digit 7 is in the thousands place, giving it a place value of 7,000.
| 3. Can you explain how to read and write numbers in expanded form using the place value system? | |
Ans. Reading and writing numbers in expanded form involves breaking down a number into the sum of its place values. For instance, the number 4,302 can be expressed in expanded form as 4,000 + 300 + 0 + 2. This method highlights the contribution of each digit in the number according to its place value, making it easier to understand the number's composition.
| 4. What are some common mistakes students make when working with place value? | |
Ans. Common mistakes include misidentifying the place value of digits, especially in larger numbers, and failing to account for zeros in certain positions. For example, confusing the place value of 5 in 5,208 (where it represents five hundreds) with its value in 52 (where it represents five tens) can lead to errors. Additionally, students may overlook the significance of zero, which can change the value of a number drastically depending on its position.
| 5. How does the place value system relate to other number systems, such as binary or hexadecimal? | |
Ans. The place value system is not exclusive to the decimal system; it is also a fundamental concept in other number systems like binary and hexadecimal. In binary, each place value represents a power of 2 (e.g., 1, 2, 4, 8, etc.), while in hexadecimal, each place represents a power of 16. Understanding the place value system allows for easier conversion and manipulation of numbers across different bases, essential for fields such as computer science and digital electronics.
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