Mathematics
Decimal representation
In this Class 9 Mathematics topic from the Number Systems chapter, students learn how numbers are expressed in decimal form and how decimal expansions relate to rational and irrational numbers. They examine terminating and non-terminating decimals, identify repeating patterns, and connect decimal representations with fractions. The topic builds accuracy in comparing, interpreting, and converting numerical forms while strengthening understanding of the structure and properties of real numbers.
Topic overviewटॉपिक का परिचय
Concept revisionअवधारणाओं का पुनरावर्तन
What is Q={x∈N: x<40 and the last digit of x is 7}?
List the natural numbers whose units digit is 7: 7, 17, 27, 37, 47, and so on. Applying the strict condition x<40 keeps 7, 17, 27 and 37, but removes 47 and every larger value.
If A={x:x=2n-1, n∈N, n≤5}, what is its roster form?
Because n is a natural number and n≤5, take n=1, 2, 3, 4, and 5. Substitution in x=2n−1 gives x=1, 3, 5, 7, and 9 respectively.
How can the decimal number 0.75 be written as a fraction in simplest form?
Since 0.75 has two digits after the decimal point, it can be written as \(\frac{75}{100}\). Dividing the numerator and denominator by 25 gives \(\frac{75}{100}=\frac{3}{4}\), so option A is correct.