Envision Math Accelerated Grade 7 Volume 1 Student Edition Chapter 2 Real Numbers
Page 80 Question 1 Answer
Real numbers include rational and irrational numbers.
Real numbers help in measuring the quantities that vary continuously such as time, different from natural numbers.
Real numbers include rational and irrational numbers.
Real numbers help in measuring the quantities that vary continuously such as time, different from natural numbers.
Page 82 Exercise 1 Answer
Natural resources like water, oil, and forests are in danger of someday being depleted.
They support the industry and economy of the country.
They are useful to man or could be useful under conceivable.
Technological, economic, or social circumstances or supplies drawn from the earth, supplies such as food, building and clothing materials, fertilizers, metals, water, and geothermal power.
They are divided into renewable and non-renewable resources.
Solar power, wind power, hydropower, and other renewable resources help us to reduce the dependency on non-renewable resources like oil and fossil fuels.
Thus, natural resources are essential for human life. We should protect natural resources from depletion.
Page 83 Exercise 1 Answer
The decimal ending with repeating zeroes means it has an end.
So, a terminating decimal is a decimal that ends in repeating zeros.
A terminating decimal is a decimal that ends in repeating zeros.
Page 83 Exercise 3 Answer
A counting number is any number like 1,2,3,…
The opposite is −1,−2,−3,…
These numbers are integers. So, the sentence is given by
An integer is either a counting number, the opposite of a counting number, or zero.
An integer is either a counting number, the opposite of a counting number, or zero.
Page 83 Exercise 4 Answer
The given definition is of a function.
So the statement becomes.
A fraction is a number that can be used to describe a part of a whole, a part of a set, a location on a number line, or a division of whole numbers.
A fraction is a number that can be used to describe a part of a whole, a part of a set, a location on a number line, or a division of whole numbers.
Page 83 Exercise 5 Answer
The given number is 5.692.
Note that there are no dots after the last decimal digit 2, which means there are no digits after this.
So the given number is terminating decimal.
The given number 5.692 is a terminating decimal.
Page 83 Exercise 6 Answer
The given number is −0.222222…
Note that there are dots after the last decimal digit 2, which means there are infinite digits after this.
So the given number is repeating decimal.
The given number −0.222222… is a repeating decimal.
Page 83 Exercise 7 Answer
The given number is 7.0001.
Note that there are no dots after the last decimal digit 1, which means there are no digits after this.
So the given number is terminating decimal.
The given number 7.0001 is a terminating decimal.
Page 83 Exercise 8 Answer
The given number is \(7.2 \overline{8}\).
Note that there is a bar on the last decimal digit 8, which means there are infinite digits after this.
So the given number is repeating decimal.
The given number \(7.2 \overline{8}\) is a repeating decimal.
Page 83 Exercise 9 Answer
The given number is \(1.\overline{178}\).
Note that there is a bar on the last decimal digits 178 which means there are infinite digits after this.
So, the given number is a repeating decimal.
The given number \(1.\overline{178}\) is a repeating decimal.
Page 83 Exercise 10 Answer
The given number is −4.03479.
Note that there are no dots after the last decimal digit 9, which means there are no digits after this.
So the given number is terminating decimal.
The given number −4.03479 is a terminating decimal.
Page 83 Exercise 11 Answer
The product to be found in
⇒ 2.2
Multiply the numbers
= 4
The product is given by 2.2 = 4.
Page 83 Exercise 12 Answer
The product to be found in
⇒ −5.(−5)
Multiply the numbers
= 25
The product is given by−5.(−5) = 25.
Page 83 Exercise 13 Answer
The product to be found in
⇒ 7.7
Multiply the numbers
= 49
The product is given by 7.7 = 49.
Page 83 Exercise 14 Answer
The product to be found in
⇒ −6.(−6).(−6)
Multiply the first two numbers
= 36.(−6)
Multiply the numbers
= −216
The product is given by −6. (−6). (−6)=−216.
Page 83 Exercise 16 Answer
The product to be found in
⇒ −9.(−9).(−9)
Multiply the first two numbers
= 81.(−9)
Multiply the numbers
= −729
The product is given by −9. (−9).(−9)= −729.
Page 83 Exercise 18 Answer
The product to be found in
⇒ (2.100) + (7.10)
Find the products
= 200 + 70
Find the sum
= 270
The value is given by (2.100) + (7.10) = 270.
Page 83 Exercise 19 Answer
The product to be found in
⇒ (6.100)−(1.10)
Find the products
= 600−10
Find the sum
= 590
The value is given by(6.100)−(1.10)=590.
Page 83 Exercise 20 Answer
The product to be found in
⇒ (9.1,000) + (4.10)
Find the products
= 9000 + 40
Find the sum
= 9040
The value is given by(9.1,000) + (4.10)= 9040.
Page 83 Exercise 21 Answer
The product to be found in
(3.1,000)−(2.100)
Find the products
= 3000−200
Find the sum
= 2800
The value is given by(3.1,000)−(2.100)= 2800.
Page 83 Exercise 22 Answer
The product to be found in
(2.10) + (7.100)
Find the products
= 20 + 700
Find the sum
= 720
The value is given by (2.10) + (7.100) = 720.
Page 84 Exercise 1 Answer
Objective: To give definitions and examples to each term given in graphic organizer.
Definition of cube root: Given a number x, the cube root of x is the number a such that a3 = x
Example: The cube root of 27 is 3. Since 27 = 33.
Definition of irrational number: Irrational numbers have decimal expansions that neither terminate nor become periodic.
They are any real number that cannot be expressed as the quotient of two integers.
Example: √2,1.33333333…,e
Definition of the perfect cube: The perfect cube is an integer that is equal to some other integer raised to the third power.
If x is a perfect cube of y, then x = y3.
Example: Multiplying 5 three times, we get 125. Therefore,125 is a perfect cube.
Definition of perfect square: The perfect square is an integer that is equal to some other integer raised to the second power.
If x is a perfect square of y, then x = y2.
Example: Multiplying 5 two times, we get 25. Therefore, 25 is a perfect square.
Definition of scientific notation: Scientific notation is a way of writing very large or very small numbers conveniently in decimal form.
Example: 0.00063 = 6.3 × 10−4
Definition of square root: Given a number x, the square root of x is the number a such that a2 = x
Example: The square root of 121 is 11. Since 121=112.
Hence, we have given the definitions and examples to each term in a graphic organizer.