Progressive Mathematics Learning Point

Class9: Granita Manjari
Question 10
A rational number has a terminating decimal expansion whose last non-zero digit occurs in the 4th decimal place. Show that such a number can be written in the form P) 10^4, where p is an integer not divisible by 10. Is it necessary that the denominator of this rational number, when written in the lowest form, is divisible by 2^4 or 5^4? Give reasons.

Class 9 Ganita Manjari .
Show that the rational number numbers a and b. (a+b)/2 lies between the Rational numbers a and b

Class 8 Ganit Parkash

Class 9 Ganita Manjari
12. A rational number in its lowest form has denominator 2^3 × 5. How many decimal places will its decimal expansion have?
9. Let a and b be two non-zero rational numbers such that a + 1/b = 0 . Without assigning any numerical values, determine is positive or negative. Justify your answer.

Class 9 Ganita Manjari

4. Explain, using a real-world example of debt, why subtracting a negative number is the same as adding a positive number (e.g., 10-(-5)= 10+5=15)

Class9 Granita Manjari
Ancient Indians used the joints of their fingers to count, a practice still seen today. Each finger has 3 joints, and the thumb is used to count them. How many can you count on one hand? How does this relate to the ancient base-12 counting systems?