(A) Let $x = 1.23444...$ (Equation $1$).Multiply by $100$ to shift the decimal point: $100x = 123.444...$ (Equation $2$).Multiply Equation $2$ by $10$

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(A) Let $x = 1.23444...$ (Equation $1$).Multiply by $100$ to shift the decimal point: $100x = 123.444...$ (Equation $2$).Multiply Equation $2$ by $10$ to shift the decimal point again: $1000x = 1234.444...$ (Equation $3$).Subtract Equation $2$ from Equation $3$:$1000x - 100x = 1234.444... - 123.444...$$900x = 1111$.Therefore,$x = \frac{1111}{900}$.

Class 9 Mathematics Number Systems Real Numbers and their Decimal Expansions

Medium

Express $1.23\overline{4}$ in the form $\frac{p}{q}$,where $p$ and $q$ are integers and $q \neq 0$.

A
$\frac{1111}{900}$
B
$\frac{1234}{999}$
C
$\frac{111}{90}$
D
$\frac{123}{100}$

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Number Systems

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Real Numbers and their Decimal Expansions

Write the following in decimal form and state what kind of decimal expansion each has:
$\frac{121}{400}$

Medium

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Convert the following rational number into decimal form and state the kind of its decimal expansion:
$\frac{29}{12}$

Medium

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Express the following in the form $\frac{p}{q}$,where $p$ and $q$ are integers and $q \ne 0$.
$(i)$ $0.\overline{6}$
$(ii)$ $0.4\overline{7}$
$(iii)$ $0.\overline{001}$

Medium

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Express the following in the form $\frac{p}{q},$ where $p$ and $q$ are integers and $q \neq 0 .$
$0 . \overline{35}$

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Fill in the blanks to make the following statement true: The decimal expansion of $\frac{2}{3}$ is of $\ldots \ldots$ type.

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Express $1.23\overline{4}$ in the form $\frac{p}{q}$,where $p$ and $q$ are integers and $q \neq 0$.

Similar Questions

Write the following in decimal form and state what kind of decimal expansion each has:$\frac{121}{400}$

Convert the following rational number into decimal form and state the kind of its decimal expansion:$\frac{29}{12}$

Express the following in the form $\frac{p}{q}$,where $p$ and $q$ are integers and $q \ne 0$.$(i)$ $0.\overline{6}$$(ii)$ $0.4\overline{7}$$(iii)$ $0.\overline{001}$

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Write the following in decimal form and state what kind of decimal expansion each has:
$\frac{121}{400}$

Convert the following rational number into decimal form and state the kind of its decimal expansion:
$\frac{29}{12}$

Express the following in the form $\frac{p}{q}$,where $p$ and $q$ are integers and $q \ne 0$.
$(i)$ $0.\overline{6}$
$(ii)$ $0.4\overline{7}$
$(iii)$ $0.\overline{001}$

Express the following in the form $\frac{p}{q},$ where $p$ and $q$ are integers and $q \neq 0 .$
$0 . \overline{35}$