Question

Express 1.419 19bar In p q form​

Answer 1

Answer:

281/198

Step-by-step explanation:

$\Rightarrow\ Let\ \ x=1.4\overline{19} \\ \\ \\ \Rightarrow\ x=1.4\overline{19} \\ \\ \Rightarrow\ 10x=14.\overline{19} \\ \\ \Rightarrow\ 1000x=1419.\overline{19} \\ \\ \Rightarrow\ 1000x-10x=1419.\overline{19}-14.\overline{19} \\ \\ \Rightarrow\ 990x=1405 \\ \\ \Rightarrow\ x=\frac{1405}{990} \\ \\ \Rightarrow\ x=\bold{\frac{281}{198}}$

Answer 2

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$let \: x = 1.4 |19|......................1 \\ \\ multiply \: 10 \: in \: equation \: 1 \: both \: side.. \\ we \: have \: .. \\ \\ 10x = 14. |19| .......................2 \\ \\ again \: multiply \: 100 \: in \: equation \: 2 \: both \: side \: .. \\ we \: have \: .. \\ \\ 1000x = 1419. |19| ........................3\\ \\ now \: subtract \: equation \: 2 \: from \: 3.. \\ we \: have... \\ \\ 1000x - 10x = 14. |19| - 1419. |19| \\ \\ 990x = 1405.0 \\ \\ x = \frac{1405}{990} \\ \\ x = \frac{281}{198}$

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$\huge {\bold {\orange {hope \: it \: helps}}}$