Rational numbers are fractions and their opposites. All of these numbers are rational numbers. Show that they are rational by writing them in the form a/b or -a/b.
0.2-1/5
-√4
0.333-333/1000
√100
-1.000001
√1/9
All rational numbers have decimal representations, too. Find the decimal representation of each of these rational numbers.
3/8
7/5
999/1000
111/2
3√1/8
Problem 4
Write each fraction as a decimal.
√9/100
99/100
√9/16
23/10
Rational numbers are fractions and their opposites. All of these numbers are rational numbers. Show that they are rational by writing them in the form a/b or -a/b.
0.2 = -1/5 That is 2/10 - 1/5 = 1/5 - 1/5 = 0
-√4 = -√2^2 = -2/1
0.333 = 333/1000
√100 = √10^2 = 10/1
-1.000001 = -1000001/ 1000000
√1/9 = √1^2/3^2 = 1/3
All rational numbers have decimal representations, too. Find the decimal representation of each of these rational numbers.
3/8 = .375 do with calculator or type into search engine 3/8=
7/5 = 1 + 2/5 = 1 + 4/10 = 1.4
999/1000 = 0.999
111/2 = 110/2 + 1/2 = 55.5
3√1/8 = 3 √(1/2 *1/4) = (1.5) √1/2 = not rational because square root 2 is not rational
= 1.060660172....... etc
Problem 4
Write each fraction as a decimal.
√9/100 0.09
99/100 0.99
√9/16 = 3/4 = 0.75
23/10 = 2.3
To show that a number is rational, we need to express it in the form a/b or -a/b, where a and b are integers (b ≠ 0). Let's address each question individually.
Question 1: 0.2 - 1/5
To write this as a fraction, we'll first convert 0.2 to a fraction. Since 0.2 is equivalent to 2/10 or 1/5, we can write the expression as 1/5 - 1/5. This simplifies to 0, which can be expressed as 0/1.
Question 2: -√4
√4 equals 2 since the square root of a perfect square is an integer. Therefore, -√4 can be written as -2/1.
Question 3: 0.333 - 333/1000
To convert 0.333 to a fraction, we'll write it as 333/1000. Now the expression becomes 333/1000 - 333/1000, which simplifies to 0.
Question 4: √100
√100 equals 10 since the square root of a perfect square is an integer. Thus, √100 can be written as 10/1.
Question 5: -1.000001
Since -1.000001 is already in decimal form, it can be expressed as -1000001/1000000 by shifting the decimal point six places to the left.
Question 6: √1/9
√1/9 can be written as 1/3 since the square root of 1 is 1, and the square root of 9 is 3.
Now, let's find the decimal representations of the given rational numbers.
Question 1: 3/8
To convert this fraction into a decimal, divide 3 by 8: 3 ÷ 8 = 0.375.
Question 2: 7/5
Divide 7 by 5: 7 ÷ 5 = 1.4.
Question 3: 999/1000
Divide 999 by 1000: 999 ÷ 1000 = 0.999.
Question 4: 111/2
Divide 111 by 2: 111 ÷ 2 = 55.5.
Question 5: 3√1/8
To convert this expression into a decimal, we first evaluate the cube root of 1/8. The cube root of 1 is 1, and the cube root of 8 is 2. So the expression becomes 3 × 1/2 = 3/2 = 1.5.
Problem 4:
Question 1: √9/100
√9 equals 3 since the square root of a perfect square is an integer. Thus, √9/100 can be written as 3/10.
Question 2: 99/100
This fraction is already in decimal form, so the decimal representation is 0.99.
Question 3: √9/16
√9 equals 3 since the square root of a perfect square is an integer. Therefore, √9/16 can be written as 3/4.
Question 4: 23/10
This fraction is already in decimal form, so the decimal representation is 2.3.
I hope this helps! If you have any further questions, feel free to ask.