Experts have designed these Class 7 Maths Notes and Part 2 Chapter 4 Another Peek Beyond the Point Class 7 Notes for effective learning.
Class 7 Maths Chapter 4 Another Peek Beyond the Point Notes
Class 7 Another Peek Beyond the Point Notes
→ In the earlier chapter ‘A Peek Beyond the Point’, a unit can be divided into smaller parts such as tenths \((\frac{1}{10}\right)\), hundredths \(\left(\frac{1}{100}\right)\), thousandths \((\frac{1}{1000}\right)\), and so on to obtain more accurate measurements. These are the decimal fractions. In decimal numbers, the decimal point (.) and separates the whole number part from the fractional part in the Indian place value system.
Additionally, we can read, write, and compare them as counting numbers. Decimal numbers can be represented on the number line as we represent fractions. Performing operations on decimal numbers are extension of the procedures for performing operations on counting numbers.
→ For decimal multiplication, we first multiply the multiplier and multiplicand as counting numbers. The number of decimal places in the product is the total number of decimal places in the multiplier and the multiplicand.
→ The relationship between the numbers multiplied and the product is similar to that of fractions:
- When both numbers are greater than 1 , then the product is greater than both numbers.
- When both numbers are between 0 and 1 , then the product is less than both numbers.
- When one number is between 0 and 1 , and the other is greater than 1, then the product is less than the number greater than 1 and greater than the number between 0 and 1.
→Division of decimals follows the same method as division of counting numbers, using place value (long division).
→ The regrouping continues beyond the Ones place to Tenths, Hundredths, Thousandths, and so on.
→ A decimal point is placed in the quotient when the Ones are regrouped into Tenths.
→ When we divide two counting numbers, the quotient is always less than or equal to the dividend.
→When the divisor is a decimal number, the quotient can also be greater than the dividend.
→ In some decimal divisions, the quotient goes on endlessly. After each regrouping and dividing there is always a remainder remains.