Question

plot \\(\sqrt{97}\\) on the decimal number line as accurately as possible. note that you can use the calculator to help find the answer.

Explanation:

Step1: Calculate √97

We know that \( 9^2 = 81 \) and \( 10^2 = 100 \). Using a calculator, \( \sqrt{97} \approx 9.849 \).

Step2: Analyze the number line

The number line is from 9 to 10, with 10 equal intervals (since there are 10 marks between 9 and 10). Each interval represents \( \frac{10 - 9}{10}=0.1 \).

Step3: Locate the position

Since \( \sqrt{97}\approx9.849 \), we move 8 full intervals (8*0.1 = 0.8, so 9 + 0.8 = 9.8) and then about 0.049 more towards the next interval (which is 9.9). So it's close to 9.85, which is 8.5 intervals from 9 (since 0.85 / 0.1 = 8.5). So on the number line, we place the dot 8.5 intervals from 9 (or 1.5 intervals from 10).

Answer:

To plot \( \sqrt{97} \) on the number line:

1. Calculate \( \sqrt{97} \approx 9.849 \).
2. On the number line from 9 to 10 (with 10 equal parts, each 0.1), place the dot 8.5 parts (or 0.85 units) to the right of 9 (or 1.5 parts to the left of 10). So the dot should be between the 8th and 9th mark after 9 (closer to the 9th mark, as 0.849 is very close to 0.85).