Using a number line, what is the approximate number value of 103√ ? Provide your answer in decimal form, rounded to the nearest hundredth.

Answer 1

To find the approximate number value of $\sqrt{103}$, we can use a number line:

[asy]
unitsize(0.1 cm);

int i;

draw((-2,0)--(2,0));
draw((0,-2)--(0,2));

for (i = -2; i <= 2; ++i) {
draw((i,-0.2)--(i,0.2));
}

label("$0$", (0,-0.2), S);
label("$1$", (1,-0.2), S);
label("$2$", (2,-0.2), S);

label("$\sqrt{103}$", (10*sqrt(103)/20,2), N);
draw(interp((0,-2),(10*sqrt(103)/20,0),0.1)--interp((0,-2),(10*sqrt(103)/20,0),-0.1),darkred+linewidth(1.5));
[/asy]

We see that $\sqrt{100} = 10$, so $\sqrt{103}$ is slightly greater than 10, but less than 11. Therefore, the approximate number value of $\sqrt{103}$ is $\boxed{10.15}$, rounded to the nearest hundredth.