Question

maths number system 9th problem. Please give step by step explanation

Answer 1

$\red{\bigstar}$Property of equations.

If two numbers are connected in the '=' sign, two numbers are equal and addition/subtraction/multiplication/division(by non-zero numbers) by an equal value keeps the equality. However this is not restricted to only numbers, we can do the same to the equations.

$\large\underline{\text{How to construct an equation?}}$

Let the number be $x$. A fractional part can be subtracted by another fractional part.

$\iff10x=43.\overline{3}\cdots\ \text{(Equation [1])}$

$\iff x=4.\overline{3}\cdots\ \text{(Equation [2])}$

$\green{\bigstar}$Property of equations in use.

Now we can construct an equation. We know that subtracting by an equal number keeps the equality.

By subtracting $\text{Equation [1]}$ by $\text{Equation [2]}$, we get,

$\iff10x-x=43.\overline{3}-4.\overline{3}$

Solving the equation we get,

$\iff9x=39$

$\iff x=\dfrac{39}{9}$

$\iff\large\boxed{x=\dfrac{13}{3}}$

Hence $4.\overline{3}$ in the lowest terms is $\large\dfrac{13}{3}$.

Answer 2

STEP-BY-STEP EXPLANATION:

.

$\sf Let \: The \: number \: given \: be \: x.$

$\sf So,$

$\implies\color{lime}\sf x = 4. \bar{3}$

$\sf Multiply \: 10 \: both \: sides,$

$\implies\color{purple}\sf 10x = 10(4. \bar{ 3})$

$\implies\color{purple}\sf 10x = 43. \bar{ 3}$

$\implies\color{purple}\sf 10x = 39 + 4. \bar{ 3}$

$\sf As \: we \: know \: that,$

$\implies\color{lime}\sf 4. \bar{3} = x$

$\sf Finding \: The \: value \: of \: x,$

$\implies \color{orange}\sf 10x = 39 + 4. \bar{ 3}$

$\implies\color{orange}\sf 10x = 39 + x$

$\implies\color{orange}\sf 10x - x= 39$

$\implies\color{orange}\sf 9x = 39$

$\implies\color{orange}\sf x = \frac{39}{9}$

$\implies\color{red}\sf x = \frac{13}{3}$

$\sf As \: we \: know \: that,$

$\implies \color{lime}\sf x = 4. \bar{3}$

$\sf Therefore,$

$\implies \color{red} \boxed{\tt 4. \bar{3} = \frac{13}{3} }$

REQUIRED ANSWER,

.

• $\color{blue}\sf In \: \: \frac{p}{q} \: \: form, \: \: 4.\bar{3} \: \: is \: \: \frac{13}{3}.$