Using a number line, what whole number and rational number to the nearest half is √97 between?
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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)
incorrect on both th top answer and this one
nevermind on the top one you just have to swich the numbers st il wrong on the bottem one though
Finding the whole number and rational number to the nearest half that √97 is between:
First, let's find the whole number that √97 is nearest to. Squaring whole numbers, we have:
9^2 = 81
10^2 = 100
Since 97 is closer to 100, the whole number to the nearest half is 10.
Now let's find the rational number to the nearest half. To do this, we'll compare the value of √97 to √100 and √81:
√81 = 9
√100 = 10
Since 97 is closer to 100, the rational number to the nearest half is between 9 and 10. Let's find the halfway point:
9 + (10 - 9)/2 = 9.5
Therefore, √97 is between the whole number 10 and the rational number 9.5.
To find the approximate decimal value of √103 on a number line, we can use the following steps:
First, let's estimate the whole number that √103 is closest to. Squaring whole numbers, we have:
10^2 = 100
11^2 = 121
Since 103 is closer to 100, the whole number for √103 is 10.
To refine our estimate, let's divide the number line segment between 10 and 11 into smaller increments. We can divide it by tenths, represented by decimal numbers.
Next, we can estimate the location of √103 on the number line. To do this, we can examine the size of the number relative to √100 (which is 10):
√103 is closer to √100 than √121.
Let's calculate the decimal representation by getting the midpoint between 10 and 11:
10 + (11-10)/2 = 10.5
Therefore, the approximate decimal value of √103, rounded to the nearest hundredth, is 10.50.