Mathematics
Decimal expansion of rational numbers
परिमेय संख्याओं का दशमलव प्रसार
In Class 10 Mathematics, this topic from the Real Numbers chapter explains how rational numbers are represented in decimal form. Students learn to distinguish terminating decimals from non-terminating recurring decimals and determine the type of expansion by reducing a fraction to its simplest form and examining the prime factors of its denominator. The topic also develops accuracy in long division, fraction-to-decimal conversion, and understanding the relationship between rational numbers and their decimal representations.
Practice questions
If the reduced denominator still has the factor (3), what type of decimal expansion will the rational number have?After how many places will the decimal expansion of (\frac{17}{160}) terminate?After how many decimal places will the decimal expansion of (\frac{7}{625}) terminate?After how many places does the decimal expansion of (\frac{1}{40}) terminate?If a fraction in lowest form has denominator (2500), after at most how many places will its decimal expansion terminate?If the decimal expansion of (\frac{7}{2^2\times5^x}) terminates exactly after (6) places, what is the value of (x)?What should be done first while deciding the type of decimal expansion?What is the correct type of decimal expansion of (\frac{44}{105})?Choose the correct option for (\frac{75}{300}).If (\frac{p}{q}) is in lowest form and its decimal expansion is terminating, what is the correct statement about (q)?A decimal that terminates exactly after (2) places can always be written as a fraction with which denominator?What is the simplest fractional form of (0.125)?Which is the simplest fractional form of (0.\overline{27})?Which is the correct fractional form of (0.2\overline{3})?When (4.125) is written as a fraction in lowest form, what will its denominator be like?Choose the correct statement about the decimal expansion (3.1416).Which statement is correct about a non-terminating non-recurring decimal?After how many places will the decimal expansion of (\frac{1}{2^5}) terminate?After reducing (\frac{15}{48}), after how many places will its decimal expansion terminate?What is the decimal form of (\frac{18}{125})?