Just do it in 5 seconds!

Number Theory Level 1

$\large \begin{aligned} \color{#3D99F6} 9797 \color{#333333} ÷ \color{#D61F06} 97 \color{#333333} & = \color{#20A900} 101 \\ \large \color{#3D99F6} 9898 \color{#333333} ÷ \color{#D61F06} 98 \color{#333333} & = \color{#20A900} 101 \\ \large \color{#3D99F6} 9999 \color{#333333} ÷ \color{#D61F06} 99 \color{#333333} & = \color{#20A900} 101 \\ \\ \color{#3D99F6} 100100 \color{#333333} ÷ \color{#D61F06} 100 \color{#333333} & = \color{#69047E} \boxed{x} \end{aligned}$

What is the value of $\color{#69047E} x$ ?

BONUS: Explain why this happens.