To find the approximate value of √103 using a number line, we can start by locating the square root of 100 and the square root of 121 on the number line.
The square root of 100 is 10, and the square root of 121 is 11. So, we know that the value of √103 is between 10 and 11 on the number line.
To get a more precise approximation, we can divide the number line between 10 and 11 into smaller intervals. Let's divide it into tenths.
10.0 10.1 10.2 10.3 10.4 10.5 10.6 10.7 10.8 10.9 11.0
Based on the square root of 103 being between 10 and 11, we can determine that it is closer to 10.1 since 10.1 squared (10.1 * 10.1) is 102.01, which is just under 103.
Therefore, the approximate number value of √103 is 10.1 (rounded to the nearest hundredth).
Using a number line, what is the approximate number value of 103−−−√ ? Provide your answer in decimal form, rounded to the nearest hundredth.
5 answers
are you sure
Apologies for the confusion. Let's recalculate the approximate value of √103 using a number line.
We know that the square root of 100 is 10 and the square root of 121 is 11.
Let's divide the number line between 10 and 11 into smaller intervals, this time by hundredths:
10.00 10.01 10.02 10.03 ... 10.97 10.98 10.99 11.00
To determine where √103 lies, we can compare the squares of the numbers on the number line to 103.
10.00^2 = 100.00
10.01^2 = 100.2001
10.02^2 = 100.4004
...
10.96^2 = 103.3216
10.97^2 = 103.3529
10.98^2 = 103.3844
10.99^2 = 103.4161
From this calculation, we can see that the square root of 103 is closer to 10.2 than to 10.3. Therefore, the approximate number value of √103 is 10.20 (rounded to the nearest hundredth).
We know that the square root of 100 is 10 and the square root of 121 is 11.
Let's divide the number line between 10 and 11 into smaller intervals, this time by hundredths:
10.00 10.01 10.02 10.03 ... 10.97 10.98 10.99 11.00
To determine where √103 lies, we can compare the squares of the numbers on the number line to 103.
10.00^2 = 100.00
10.01^2 = 100.2001
10.02^2 = 100.4004
...
10.96^2 = 103.3216
10.97^2 = 103.3529
10.98^2 = 103.3844
10.99^2 = 103.4161
From this calculation, we can see that the square root of 103 is closer to 10.2 than to 10.3. Therefore, the approximate number value of √103 is 10.20 (rounded to the nearest hundredth).
wrong
I apologize for the previous incorrect responses. Let's recalculate the approximate value of √103 using a number line.
Since the square root of 100 is 10 and the square root of 121 is 11, we can divide the number line between 10 and 11 into smaller intervals.
Let's divide the number line into tenths:
10.0 10.1 10.2 10.3 10.4 10.5 10.6 10.7 10.8 10.9 11.0
To find where √103 lies, we can compare the squares of the numbers on the number line to 103.
10.0^2 = 100
10.1^2 = 102.01
10.2^2 = 104.04
Based on these calculations, we can see that the square root of 103 is closer to 10.1 than to 10.2. Therefore, the approximate number value of √103 is 10.10 (rounded to the nearest hundredth).
Since the square root of 100 is 10 and the square root of 121 is 11, we can divide the number line between 10 and 11 into smaller intervals.
Let's divide the number line into tenths:
10.0 10.1 10.2 10.3 10.4 10.5 10.6 10.7 10.8 10.9 11.0
To find where √103 lies, we can compare the squares of the numbers on the number line to 103.
10.0^2 = 100
10.1^2 = 102.01
10.2^2 = 104.04
Based on these calculations, we can see that the square root of 103 is closer to 10.1 than to 10.2. Therefore, the approximate number value of √103 is 10.10 (rounded to the nearest hundredth).
6 answers