Question
Insert $16$ rational numbers between $2.1$ and $2.2$.
✓
Answer
Let: $x = 2.1, y = 2.2$ and $n = 16$
We know: $\text{d}=\frac{\text{y}-\text{x}}{\text{n}+1}=\frac{2.2-2.1}{16+1}=\frac{0.1}{17}=\frac{1}{170}=0.005\text{(approx.)}$
So, $16$ rational numbers between $2.1$ and $2.2$ are: $(x + d), (x + 2d),...(x + 16d) = [2.1 + 0.005], [2.1 + 2(0.005)],...[2.1 + 16(0.005)] = 2.105, 2.11, 2.115, 2.12, 2.125, 2.13, 2.135, 2.14, 2.145, 2.15, 2.155, 2.16, 2.165, 2.17, 2.175$ and $2.18$.
We know: $\text{d}=\frac{\text{y}-\text{x}}{\text{n}+1}=\frac{2.2-2.1}{16+1}=\frac{0.1}{17}=\frac{1}{170}=0.005\text{(approx.)}$
So, $16$ rational numbers between $2.1$ and $2.2$ are: $(x + d), (x + 2d),...(x + 16d) = [2.1 + 0.005], [2.1 + 2(0.005)],...[2.1 + 16(0.005)] = 2.105, 2.11, 2.115, 2.12, 2.125, 2.13, 2.135, 2.14, 2.145, 2.15, 2.155, 2.16, 2.165, 2.17, 2.175$ and $2.18$.
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