Using a number line what is the approximate number value of ✓103 provide your answer in decimal form rounded to the nearest hundredth
To find the approximate number value of √103 on a number line, we can make an estimate.
First, we know that √100 is equal to 10 since 10 multiplied by itself is 100. This gives us a reference point on the number line.
Next, we can locate √103 on the number line by estimating the distance between √100 and √121. √121 is equal to 11 since 11 multiplied by itself is 121.
The distance between √100 and √121 can be divided evenly into 20 equal parts since 11 - 10 = 1. Therefore, each part represents 1/20 or 0.05.
Since √103 is approximately 10.15 (as it falls just past the midpoint between √100 and √121), we can estimate that it is approximately 10 + 0.15 or 10.15 on the number line.
Rounded to the nearest hundredth, the approximate number value of √103 is 10.15.
To find the approximate decimal value of √103 using a number line, follow these steps:
1. Start by placing the number 103 on the number line.
2. Estimate the position of the square root (√) of 103 on the number line. Since square roots are between the nearest perfect squares, √103 would be approximately between √100 and √121.
3. The square root of 100 is 10, and the square root of 121 is 11.
4. Therefore, the approximate position of √103 on the number line is between 10 and 11.
5. To find the decimal form rounded to the nearest hundredth, we can divide 103 by 10 and get a decimal value.
6. Calculating the division, 103 ÷ 10 = 10.3.
7. So, the approximate decimal value of √103, rounded to the nearest hundredth, is 10.3.