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Find $7$ rational numbers between $2$ and $3$ at equal intervals

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Full solution

Q. Find

7

rational numbers between

2

and

3

at equal intervals

Divide Interval into Parts: To find $7$ rational numbers between $2$ and $3$ , we need to divide the interval from $2$ to $3$ into $8$ equal parts.
Calculate Increment Value: The difference between $3$ and $2$ is $1$ . To divide this into $8$ equal parts, we divide $1$ by $8$ . $\newline$ $1 \div 8 = 0.125$
Find First Rational Number: Now, we add $0.125$ to $2$ to find the first rational number. $\newline$ $2 + 0.125 = 2.125$
Find Next Numbers: Keep adding $0.125$ to find the next numbers. $\newline$ $2.125 + 0.125 = 2.250$ $\newline$ $2.250 + 0.125 = 2.375$ $\newline$ $2.375 + 0.125 = 2.500$ $\newline$ $2.500 + 0.125 = 2.625$ $\newline$ $2.625 + 0.125 = 2.750$ $\newline$ $2.750 + 0.125 = 2.875$
Check Last Number: Check if the last number is less than $3$ . $\newline$ $2.875 + 0.125 = 3.000$ $\newline$ Since $3.000$ is not less than $3$ , we have found the correct number of rational numbers between $2$ and $3$ .

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