Using the number line what is the approximate number value of square 103 provide your answer in decimal form rounded to the nearest tenth
To find the approximate decimal value of the square root of 103, we can use the number line to estimate its value.
The number line shows that the square root of 100 is 10, and the square root of 121 is 11. Therefore, the square root of 103 is approximately between 10 and 11.
To obtain a more precise estimate, we can divide 103 into ranges of consecutive perfect squares. Since 81 (9^2) is the largest perfect square smaller than 103, we can divide the number line between 9 and 10 into 10 equal parts.
Each part represents a value of 1, so the divisions on the number line would be: 9, 9.1, 9.2, 9.3, 9.4, 9.5, 9.6, 9.7, 9.8, 9.9, 10.
Since 103 is closer to 100 than to 121, we can estimate that the square root of 103 is closer to 10 than to 11.
Therefore, the approximate decimal value of the square root of 103, rounded to the nearest tenth, is 10.1.
Using a number line what whole number and rational number to the nearest half is square 10 between
To find the whole number and rational number to the nearest half that square root of 10 (sqrt(10)) is between, we can use a number line.
The number line shows that the square root of 9 is 3 (since 3^2 = 9) and the square root of 16 is 4 (since 4^2 = 16).
Therefore, we know that sqrt(10) is between 3 and 4 on the number line.
To find the whole number and rational number to the nearest half, we can divide the space between 3 and 4 into two equal parts.
These divisions on the number line would be: 3, 3.5, 4.
Since sqrt(10) is closer to 3.5 than to 4, the whole number and rational number to the nearest half that sqrt(10) is between is 3.5.
To find the approximate value of the square root of 103 on a number line, we can start by estimating the square root of the closest perfect squares to 103. The two perfect squares closest to 103 are 100 (whose square root is 10) and 121 (whose square root is 11).
Since 103 is closer to 100 than to 121, we can estimate the square root of 103 as being closer to 10. To find a more precise estimate, we can divide 103 by 10:
103 / 10 ≈ 10.3
So the approximate value of the square root of 103, rounded to the nearest tenth, is 10.3.