Mathematics
Decimal representation
दशमलव निरूपण
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.
Practice questions
Which decimal is less than ( \frac{23}{32} ) but greater than (0.718)?ExpertLevel 10For a rational number \(\frac{p}{q}\), where \(p\) and \(q\) are coprime, when will its decimal expansion be non-terminating recurring?ExpertLevel 10What is the decimal form of ( \frac{149}{16000} )?ExpertLevel 10What is obtained when (0.00021875) is converted into a simplified fraction?ExpertLevel 10Which is the ordinary decimal form of (0.04\overline{81})?ExpertLevel 10If p/q is in simplest form and q = 2^8 × 5^11, what is the maximum number of decimal places in the terminating decimal?MediumLevel 10What is the decimal form of ( \frac{127}{3200} )?ExpertLevel 11What is obtained when (0.00009375) is converted into a simplified fraction?ExpertLevel 11If ( \frac{p}{q} ) is in simplest form and (q=2^3\times5^2\times19), what type of decimal expansion will it have?ExpertLevel 11After simplifying (198/330), what type of decimal expansion will it have?MediumLevel 11Which is the correct bar notation of (0.560909090\ldots)?ExpertLevel 11How is (4.108\overline{27}) written in ordinary decimal form?ExpertLevel 11If the rational number \(\frac{p}{q}\) is in lowest form and \(q>0\), when does its decimal expansion terminate?ExpertLevel 11Among (0.6471), ( \frac{11}{17} ), and (0.6470\overline{58}), which is the greatest number?ExpertLevel 11If (0.83a2<0.8352), what can be the greatest value of digit (a)?ExpertLevel 11What type of decimal is (9.01001000100001\ldots)?ExpertLevel 11What is the decimal form of ( \frac{77}{1024} )?ExpertLevel 11What is obtained when (0.00046875) is converted into a simplified fraction?ExpertLevel 11What type of decimal expansion will ( \frac{47}{72} ) have?ExpertLevel 11Which is the expanded form of (6.400004)?ExpertLevel 11