MATHEMATICS Textbook for Class IX>Chapter 1 - Number Systems>EXERCISE>Q 1

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Write $\frac{2}{11}$ in decimal form and say what kind of decimal expansion it has?

Important Questions on Number Systems

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IMPORTANT

MATHEMATICS Textbook for Class IX>Chapter 1 - Number Systems>EXERCISE>Q 1

Write

\frac{329}{400}

in decimal form and say what kind of decimal expansion it has?

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MATHEMATICS Textbook for Class IX>Chapter 1 - Number Systems>EXERCISE>Q 2

You know that

\frac{1}{7} = 0 . \bar{142857}

. 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?

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MATHEMATICS Textbook for Class IX>Chapter 1 - Number Systems>EXERCISE>Q 3

Express

0 . \bar{6}

in the form

\frac{p}{q}

(in the simplest form), where

p

and

q

are integers and

q \neq 0 .

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MATHEMATICS Textbook for Class IX>Chapter 1 - Number Systems>EXERCISE>Q 3

Express $0.47$ in the form $\frac{p}{q}$ , where $p$ and $q$ are integers and $q \neq 0$ .

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MATHEMATICS Textbook for Class IX>Chapter 1 - Number Systems>EXERCISE>Q 3

If

0.001

is expressed in the simplest form as

\frac{p}{q},

where

p

and

q

are integers and

q \neq 0

, then find the value of

p + q

.

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MATHEMATICS Textbook for Class IX>Chapter 1 - Number Systems>EXERCISE>Q 4

Express

0.99999 \dots \dots

in the form

\frac{p}{q} .

Are you surprised by your answer? With your teacher and classmates discuss why the answer makes sense.

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MATHEMATICS Textbook for Class IX>Chapter 1 - Number Systems>EXERCISE>Q 5

What can the maximum number of digits be in the repeating block of digits in the decimal expansion of

\frac{1}{17} ?

Perform the division to check your answer.

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MATHEMATICS Textbook for Class IX>Chapter 1 - Number Systems>EXERCISE>Q 6

Look at several examples of rational numbers in the form

\frac{p}{q} (q \neq 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?