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
What is the decimal form of 313/128000?MediumLevel 12What is obtained when (0.00003125) is converted into a simplified fraction?ExpertLevel 12If ( \frac{p}{q} ) is in simplest form and (q=2^7\times5^4\times29), what type of decimal expansion will it have?ExpertLevel 12Which is the correct bar notation of (0.000919191\ldots)?ExpertLevel 12Which of the following rational numbers will have a terminating decimal expansion when written in its simplest form?ExpertLevel 12If p/q is in simplest form and q = 2⁹ × 5¹², what is the maximum number of decimal places in the terminating decimal?HardLevel 12Which decimal is rational?EasyLevel 16Which option is a non-terminating, non-recurring decimal?EasyLevel 16Which option will have a terminating decimal expansion?MediumLevel 13Which decimal can be considered an example of an irrational number?MediumLevel 13Which statement is correct about the decimal expansion of \(\frac{13}{40}\)?ExpertLevel 19A student says that the decimal expansion of \(\frac{77}{600}\) will terminate because it is a rational number. Which is the correct analysis of the student's error?ExpertLevel 19The decimal expansion of \(\frac{7}{2^2\times5^3}\) will terminate after how many decimal places?ExpertLevel 19What type of decimal expansion does \(\frac{1}{7}\) have?ExpertLevel 19A student says that the decimal expansion of \(\frac{13}{375}\) terminates because its denominator has a factor of 5. Which correction to the student's error is correct?ExpertLevel 19How many decimal places will \(\frac{3}{2^4\times5^2}\) have when converted into decimal?ExpertLevel 19Which of the following rational numbers will have a terminating decimal expansion?ExpertLevel 19A student says, “If the decimal expansion of a rational number is non-terminating, then the number is irrational.” Which of the following numbers most clearly shows the error in this statement?ExpertLevel 19If
p/q
is a rational number and p and q are coprime, when will its decimal expansion terminate?ExpertLevel 19A student says that if the denominator of a fraction in lowest terms has 5 as a factor, then its decimal expansion terminates. Which fraction disproves the statement?ExpertLevel 19