Using a number line, what whole number and rational number to the nearest half is
√59 between?
8.5 and 9?
6 and 6.5?
7 and 7.5?
7.5 and 8?
To find whole numbers and rational numbers that are nearest to √59, we can start by finding the two perfect squares that √59 is between.
The perfect squares closest to 59 are 49 (7^2) and 64 (8^2).
Between 49 and 64, we can find the whole numbers and rational numbers to the nearest half by dividing the range into intervals of length 1.
8.5 and 9:
49 is closer to 50 (8.5^2) than 9 (3^2), so √59 is between 8 and 8.5.
6 and 6.5:
49 is closer to 6 (2^2) than 6.5 (13/4)^2, so √59 is between 6 and 6.5.
7 and 7.5:
49 is closer to 49 (7^2) than 7.5 (15/2)^2, so √59 is between 7 and 7.5.
7.5 and 8:
59 is closer to 64 (8^2) than 7.5 (15/2)^2, so √59 is between 7.5 and 8.
Write 4,739 in expanded form.
4,739 can be written in expanded form as:
4 x 1,000 + 7 x 100 + 3 x 10 + 9 x 1
or
4,000 + 700 + 30 + 9
Convert .4545454545........ to a rational number in simplest form.
To convert the repeating decimal .4545454545... to a rational number in simplest form, we can use the property of repeating decimals and define it as the fraction "x" where "x" equals .4545454545...:
10x = 4.545454545...
Subtracting the two equations, we can eliminate the repeating decimals:
10x - x = 4.545454545... - .4545454545...
Simplifying, we get:
9x = 4.090909090...
Now, we divide both sides by 9:
9x/9 = 4.090909090.../9
x = 4.090909...
Simplifying further, we can define "x" as:
x = 4.09
To express 4.09 as a rational number, we can rewrite it as a fraction by placing it over a denominator of 1:
x = 4.09/1
So, the rational number equivalent of .4545454545... is 4.09/1, which can also be simplified as 409/100 in simplest form.
Find a rational number (in simplest form) between 6 and 6 1/4?
To find a rational number between 6 and 6 1/4, we can take the average of the two numbers.
The average of 6 and 6 1/4 can be found by adding them together and dividing by 2:
((6 + 6 1/4) / 2) = (6 + 25/4) / 2
To ensure a rational number in simplest form, we can convert the mixed number 6 1/4 to an improper fraction:
(6 + 25/4) / 2 = (24/4 + 25/4) / 2 = (49/4) / 2 = 49/8
So, a rational number (in simplest form) between 6 and 6 1/4 is 49/8.