Using a number line, what is the approximate number value of √103? Provide your answer in decimal form, rounded to the nearest hundredth.
√103 is approximately __
√103 is approximately 10.15.
To find the approximate value of √103 using a number line, we need to estimate the position of the square root of 103 on the number line.
Step 1: Locate the integers on the number line. We know that 103 is between the perfect squares of 100 (10²) and 121 (11²).
Step 2: Estimate the position of √103. Since 10² = 100 and 11² = 121, we can estimate that √103 is closer to 10 than 11 on the number line.
Step 3: Now, we need to find a more precise estimate. To do this, we can divide the interval between 10 and 11 into smaller parts.
Step 4: Let's divide the interval into 10 equal parts. This means we can divide the interval between 10 and 11 into 0.1 parts.
Step 5: Start from 10 and count 0.1 intervals until we reach the approximate position of √103 on the number line.
10 + 0.1 = 10.1
10.1 + 0.1 = 10.2
10.2 + 0.1 = 10.3
10.3 + 0.1 = 10.4
10.4 + 0.1 = 10.5
10.5 + 0.1 = 10.6
10.6 + 0.1 = 10.7
10.7 + 0.1 = 10.8
10.8 + 0.1 = 10.9
10.9 + 0.1 = 11
Step 6: Based on our estimation, √103 is approximately located between 10.7 and 10.8 on the number line.
Step 7: To provide the answer in decimal form, rounded to the nearest hundredth, we can choose the midpoint between 10.7 and 10.8, which is 10.75.
Therefore, √103 is approximately 10.75.