Look at several examples of rational numbers in the form \(\frac{p}{q}\) (q ≠ 0), where p and q are integers with no common factors other than 1 and having terminating decimal representations (expansions). Can you guess what property q must satisfy?
Look at several examples of rational numbers in the form \(\frac{p}{q}\) (q ≠ 0), where p and q are integers with no common factors other than 1 and having terminating decimal representations (expansions). Can you guess what property q must satisfy?
Solution and Explanation
Terminating decimal expansion will occur when denominator q of rational number \(\frac{p}{q}\) is either of 2, 4, 5, 8, 10, and so on…
\(\frac{9}{4}\) = 2.25
\(\frac{11}{8}\) = 1.375
\(\frac{27}{5}\) = 5.4
It can be observed that terminating decimal may be obtained in the situation where prime factorisation of the denominator of the given fractions has the power of 2 only or 5 only or both.
Top Questions on Real Numbers and their Decimal Expansions
- Among \(\frac{1}{2}, \frac{1}{3}, \frac{1}{4}, \frac{1}{5}\) the non-terminating decimal is
- TS POLYCET - 2023
- Mathematics
- Real Numbers and their Decimal Expansions
Write the following in decimal form and say what kind of decimal expansion each has :
(i) \(\frac{36}{100}\) (ii) \(\frac{1}{11}\) (iii) \(4\frac{1}{8}\)
(iv) \(\frac{3}{13}\) (v) \(\frac{2}{11}\) (vi) \(\frac{329}{400}\)
- CBSE Class IX
- Mathematics
- Real Numbers and their Decimal Expansions
You know that \(\frac{1}{7}\) = 0142857_ . . Can you predict what the decimal expansions of \(\frac{2}{7},\frac{3}{7},\frac{4}{7},\frac{5}{7},\frac{6}{7}\) are, without actually doing the long division? If so, how? [Hint : Study the remainders while finding the value of 1/7 carefully.]
- CBSE Class IX
- Mathematics
- Real Numbers and their Decimal Expansions
Express the following in the form \(\frac{p }{ q}\) , where p and q are integers and q ≠ 0.
(i) 0.6(ii) 0.47 (iii) 0.001.
- CBSE Class IX
- Mathematics
- Real Numbers and their Decimal Expansions
- Express 0.99999 .... in the form \(\frac{p}{q}\) . Are you surprised by your answer? With your teacher and classmates discuss why the answer makes sense.
- CBSE Class IX
- Mathematics
- Real Numbers and their Decimal Expansions
Questions Asked in CBSE Class IX exam
(i) The kind of person the doctor is (money, possessions)
(ii) The kind of person he wants to be (appearance, ambition)- CBSE Class IX
- The snake and the mirror
- Lushkoff is earning thirty five roubles a month. How is he obliged to Sergei for this?
- CBSE Class IX
- The beggar
ABCD is a quadrilateral in which AD = BC and ∠ DAB = ∠ CBA (see Fig. 7.17). Prove that
(i) ∆ ABD ≅ ∆ BAC
(ii) BD = AC
(iii) ∠ ABD = ∠ BAC.
- CBSE Class IX
- Congruence of Triangles
- Why does the author say that Iswaran seemed to more than make up for the absence of a TV in Mahendra’s living quarters?
- CBSE Class IX
- Iswaran the storyteller
- Here is your diary entry when you visited Agra. Read the points and try to write a travelogue describing your visit to Agra and the Taj Mahal. You may add more details.
January 2003 — rise before dawn — take the Shatabdi Express at 6.15 a.m. from Delhi — meet a newly-married couple on train — talk about Himachal Pradesh — get off the train — enter the once-grand city, Agra — twisted alleys — traffic dense — rickshaws, cars, people — vendors selling religious artifacts, plastic toys, spices and sweets — go to the Taj Mahal — constructed entirely of white marble — magical quality — colour changes with varying of light and shadow — marble with gemstones inside — reflection of the Taj Mahal in the pond — school-children, tourists — tourist guides following people.- CBSE Class IX
- Kathmandu