Using a number line, what is the approximate number value of 103−−−√
? Provide your answer in decimal form, rounded to the nearest hundredth.(1 point)
The approximate number value of 103−−−√ is 10.15 (rounded to the nearest hundredth).
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To approximate the value of √103, we can use a number line. Let's start by finding two perfect squares that are close to 103.
The perfect squares closest to 103 are 100 (10^2) and 121 (11^2).
Since 103 is between these two perfect squares, we know that the square root of 103 will be between 10 and 11 on the number line.
To estimate a more accurate value, we can divide the interval between 10 and 11 into smaller intervals.
Let's divide this interval into 10 equal parts.
Each interval will represent 1/10th of the difference between 10 and 11.
The first interval will be 10 + 1/10 = 10.1
The second interval will be 10 + 2/10 = 10.2
The third interval will be 10 + 3/10 = 10.3
Continuing this pattern, we find that the tenth interval will be 10 + 10/10 = 11.
Since we are looking for the square root of 103, we need to find which interval it falls into.
To do this, we can calculate the square of each interval and see which one is closest to 103.
Calculating the squares:
10.1^2 = 102.01
10.2^2 = 104.04
10.3^2 = 106.09
From these calculations, we see that 10.3^2 = 106.09 is the closest square to 103.
Therefore, the approximate value of √103 is 10.3, rounded to the nearest hundredth.
To find the approximate value of √103, we can use a number line approach.
1. Start by writing down the number line with whole numbers and their squares:
0^2 = 0
1^2 = 1
2^2 = 4
3^2 = 9
4^2 = 16
5^2 = 25
6^2 = 36
7^2 = 49
8^2 = 64
9^2 = 81
10^2 = 100
2. Locate the number 103 on the number line. It falls between the squares of 10 and 11.
3. Since 103 is closer to 100 (10^2) than 121 (11^2), we know that the square root of 103 is closer to 10 than to 11.
4. To find the approximate decimal value, we can use estimation. Let's assume that the square root of 103 is a decimal number between 10 and 11.
5. Take a guess, such as 10.5, and square it: 10.5^2 ≈ 110.25
6. Since 110.25 is greater than 103, we need to adjust our guess downwards.
7. Let's try with a smaller guess, such as 10.4: 10.4^2 ≈ 108.16
8. Since 108.16 is still greater than 103, we can adjust our guess further downwards.
9. Let's try with an even smaller guess, such as 10.39: 10.39^2 ≈ 107.9681
10. Now, 107.9681 is smaller than 103, so we can estimate that the square root of 103 is just slightly larger than 10.39.
11. Rounding the answer to the nearest hundredth, we can say that the approximate value of √103 is 10.39.
Therefore, the approximate number value of 103−−−√ is 10.39 when rounded to the nearest hundredth.