Envision Math Grade 8 Volume 1 Student Edition Solutions Chapter 1Real Number Exercise 1.8
Page 51 Exercise 1 Answer
Given that, Keegan and Jeff did some research and found that there are approximately 7,492,000,000,000,000,000 grains of sand on Earth. Jeff says that it is about 7×1015 grains of sand. Keegan says that this is about 7×1018 grains of sand.
We need to find how might Jeff and Keegan have determined their estimates.
The amount of grains of sand is 7,492,000,000,000,000,000
Rewriting the given large quantity using a power of 10 for easy computations.
Here, Jeff considered only the zeroes of the obtained value.
This is why he estimated it about 7×1015
While Keegan considered both the zeroes and the nonzeroes after the number 7
This made him estimate the amount to be 7×1018
Jeff considered only the zeroes of the obtained value. Keegan considered both the zeroes and the nonzeroes after the number 7.
Envision Math Grade 8 Volume 1 Chapter 1 Exercise 1.8 Real Number Solutions
Page 51 Exercise 2 Answer
Given that, Keegan and Jeff did some research and found that there are approximately 7,492,000,000,000,000,000 grains of sand on Earth. Jeff says that it is about 7×1015 grains of sand. Keegan says that this is about 7×1018 grains of sand.
We need to find whose estimate, Jeff’s or Keegan’s, is more logical.
The amount of grains of sand is 7,492,000,000,000,000,000
Rewriting the given large quantity using a power of 10 for easy computations.
Here, Jeff considered only the zeroes of the obtained value.
This is why he estimated it about 7×1015
While Keegan considered both the zeroes and the nonzeroes after the number 7.
This made him estimate the amount to be 7×1018
Keegan is more logical since the non-zero values are not after the decimal point so it needs to be considered as well.
Keegan is more logical.
Envision Math Grade 8 Volume 1 Student Edition Solutions Chapter 1Real Number Exercise 1.8 Page 52 Exercise 1 Answer
We will use a power of 10 to estimate a quantity that is either too big or too small to count.
Quantities that are neither too big nor too small can easily be represented.
We have to count the number of zeroes to write it as a power of 10.
The big numbers will have a positive exponent.
The small numbers will have a negative exponent.
We can use a power of 10 to estimate a quantity when they are either too big or too small.
Envision Math Grade 8 Student Edition Exercise 1.8 Real Numbers Answers
Page 52 Exercise 1 Answer
Light travels 299,792,458 meters per second. Sound travels at 332 meters per second. We need to use power of 10 to compare the speed of light to the speed of sound.
Rounded to the greatest place value, we get,
299,792,458=300,000,000
322=300
There are 8 zeros in the rounded number 300,000,000
There are 2 zeros in the rounded number 300
The estimated speed of light is 3×108 meters per second.
The estimated speed of sound is 1×102 meters per second.
3 × 108 > 3 × 102, so the speed of light is faster than the speed of sound.
3 x 108 > 3 x 102
The speed of light is faster than the speed of sound.
Envision Math Grade 8 Volume 1 Student Edition Solutions Chapter 1Real Number Exercise 1.8 Page 53 Exercise 2 Answer
Given that, there are approximately 1,020,000,000 cars in the world. The number of cars in the United States is approximately 239,800,000.
We need to compare the number of cars in the world to that in the United States.
Rounded to the greatest place value, we get,
1,020,000,000=1,000,000,000
239,800,000=200,000,000.
There are 9 zeros in the rounded number 1,000,000,000
There are 8 zeros in the rounded number 200,000,000
The cars in the world is 1×109
The cars in US is 2×108
Thus,
1 × 109 > 2 × 108
1 x 109 > 2 x 108
The number of cars in the world is more than that of the United States.
Page 52 Exercise 1 Answer
Given that, Country A has a population of 1,238,682,005 and Country B has a population of 1,106,487,394. We need to explain how we would compare these populations.
Rounded to the greatest place value, we get,
A = 1,238,682,005 = 1,200,000,000
There are 8 zeros in the rounded number
Similarly,
B = 1,106,487,394 = 1,100,000,000
There are 8 zeros in the rounded number
The population in country A will be 12 × 108
The population in country B will be 11 × 108
Thus, 12 × 108 > 11 × 108
12 × 108 > 11 × 108
Thus, country A’s population is more.
Real Number Solutions Grade 8 Exercise 1.8 Envision Math
Envision Math Grade 8 Volume 1 Student Edition Solutions Chapter 1Real Number Exercise 1.8 Page 54 Exercise 1 Answer
We will use a power of 10 to estimate a quantity that is either too big or too small to count.
Quantities that are neither too big nor too small can easily be represented.
We have to count the number of zeroes to write it as a power of 10
The big numbers will have a positive exponent.
The small numbers will have a negative exponent.
We can use a power of 10 to estimate a quantity when they are either too big or too small.
Page 54 Exercise 5 Answer
Given that, A scientist records the mass of a proton as 0.0000000000000000000000016726231 gram. We need to use a single digit times a power of 10 to estimate the mass.
Rounded to the greatest place value, we get,
0.0000000000000000000000016726231=00000000000000000000000020000000
There are 23 zeros in the rounded number.
Thus, the value will be,
2×10-23
Since the value is less than one, the exponent is negative.
The mass of the proton is 2 x 10-23
Page 54 Exercise 6 Answer
Given that, The tanks at the Georgia Aquarium hold approximately 8.4×106 gallons of water. The tanks at the Audubon Aquarium of the Americas hold about 400,000 gallons of water. We need to use a single digit times a power of 10 to estimate how many times greater the amount of water is at the Georgia Aquarium.
Rounded to the greatest place value, we get,
400,000=400,000
There are 5 zeros in the rounded number.
Thus, it will be 21 times more.
21 times greater the amount of water is at the Georgia Aquarium.
Envision Math Grade 8 Volume 1 Student Edition Solutions Chapter 1Real Number Exercise 1.8 Page 55 Exercise 7 Answer
Given that, a city has a population of 2,549,786 people. We need to estimate this population to the nearest million. Also, express our answer as the product of a single digit and a power of 10.
Rounded to the greatest place value, we get,
2,549,786=3,000,000
There are 6 zeros in the rounded number.
Thus, the value will be,
3 × 106
The population is written as the product of a single digit and a power of ten, this number is 3 x 106
Page 55 Exercise 8 Answer
We need to use a single digit times a power of 10to estimate the number 0.00002468
Rounded to the greatest place value, we get,
0.00002468=0.00002
There are 5 zeros in the rounded number.
Thus, the value will be,
0.00002 = 2 × 10-5
The exponent is negative since the given number is less than one.
The given value is written as a single digit times a power of ten, the estimate is 2 x 10-5
Envision Math Grade 8 Chapter 1 Exercise 1.8 Solutions
Envision Math Grade 8 Volume 1 Student Edition Solutions Chapter 1Real Number Exercise 1.8 Page 55 Exercise 9 Answer
The approximate circumferences of Earth and Saturn are shown. We need to find how many times greater is the circumference of Saturn than the circumference of Earth.
The circumference of Saturn is C=365,882 km
Rounded to the greatest place value, we get, 400,000
There are 5 zeros in the rounded number.
The value will be 4×105
Thus, the circumference of Saturn is ten times more than the circumference of Earth.
The circumference of Saturn is ten times more than the circumference of Earth.
Page 55 Exercise 10 Answer
We need to estimate 0.037854921 to the nearest hundredth. We need to express your answer as a single digit times a power of ten.
Rounded to the greatest place value, we get,
0.037854921=0.04
There are 2 zeros in the rounded number.
Thus, the value will be,
4 × 10-2
The value will be 4 x 10-2
Envision Math Exercise 1.8 Real Numbers Detailed Answers
Envision Math Grade 8 Volume 1 Student Edition Solutions Chapter 1Real Number Exercise 1.8 Page 55 Exercise 11 Answer
We need to compare the numbers 6×10-6 and 2×10-8
We need to find which number has the greater value.
6 × 10-6 has the greatest value.
Envision Math 8th Grade Exercise 1.8 Step-By-Step Real Number Solutions
Envision Math Grade 8 Volume 1 Student Edition Solutions Chapter 1Real Number Exercise 1.8 Page 55 Exercise 12 Answer
Given that, Taylor made $43,785 last year. We need to ue a single digit times a power of ten to express this value rounded to the nearest ten thousand.
Rounded to the greatest place value, we get,
43,785 = 40,000
There are 4 zeros in the rounded number.
Thus, the value will be,
40,000 = 4 × 104
The value becomes 4 x 104
Page 55 Exercise 13 Answer
The length of plant cell A is 8×10-5 meter. The length of plant cell B is 0.000004 meter. We need to find how many times greater is plant cell A’s length than plant cell B’s length.
The length of plant cell B is 0.000004
20 times greatest is plant cell A’s length than plant B’s length.
Envision Math Grade 8 Exercise 1.8 Practice Problems
Envision Math Grade 8 Volume 1 Student Edition Solutions Chapter 1Real Number Exercise 1.8 Page 56 Exercise 16 Answer
Given that, Earth is approximately 5×109 years old. We need to find for which of the given ages could this be an approximation.
Rounded to the greatest place value, and converting them into the power of ten, we get,
4,762,100,000 = 5,000,000,000 = 5 × 109
4,849,000,000 = 5,000,000,000 = 5 × 109
48,000,000,000 = 50,000,000,000 = 5 × 1010
4.45 × 109 = 4 × 109
4.849999999 × 109 = 5 × 109
Earth is approximately 5×109 years old. This approximation is true for,
4,762,100,000
4,849,000,000
4.849999999 × 109
How To Solve Exercise 1.8 Real Numbers In Envision Math Grade 8
Page 56 Exercise 56 Answer
We need to express 0.000000298 as a single digit times a power of ten rounded to the nearest ten millionth.
Rounded to the greatest place value, we get,
0.000000298=0.0000003
There are 7 zeros in the rounded number.
Thus, the value will be,
3 × 10-7
The value will be 3 x 10-7
We need to explain how negative powers of 10 make small numbers easier to write and compare.
Negative powers of 10 are utilized in writing small quantities.
It will take up so much space to write very small quantities.
Here, the negative powers are used to move so many decimal spaces.
For example,
0.0000000000000004 can be written as 4 × 10-16
This will save up so much space and enables easier calculation.
While writing small numbers, each negative power of 10 will be equal to one decimal place after the decimal point.