# Math in Focus Grade 7 Chapter 1 Lesson 1.4 Answer Key Introducing the Real Number System

Go through the Math in Focus Grade 7 Workbook Answer Key Chapter 1 Lesson 1.4 Introducing the Real Number System to finish your assignments.

## Math in Focus Grade 7 Course 2 A Chapter 1 Lesson 1.4 Answer Key Introducing the Real Number System

### Math in Focus Grade 7 Chapter 1 Lesson 1.4 Guided Practice Answer Key

Represent each real number as a decimal rounded to 2 decimal places.

Question 1.
208$$\frac{12}{19}$$
208(12/19)
= (3,952 + 12)/19
= 3,964/19
=208.6315
= 208.63
Explanation:
The mixed fraction 208(12/19) in fraction form as 3,964/19. Divide 3,964 by 19 the quotient is 208.6315. The given real number as a decimal rounded to 2 decimal places is 208.63.

Question 2.
–$$\frac{456}{37}$$
-456/37
= -12.3243
= -12.32
Explanation:
Perform division operation on given real number. Divide -456 by 37 the quotient is -12.3243. The given real number as a decimal rounded to 2 decimal places is -12.32.

Question 3.

= 12.56637
= 12.57
Explanation:
Perform multiplication operation on given real number. Multiply 4 with π the product is 12.56637. The given real number as a decimal rounded to 2 decimal places is 12.57.

Represent each real number below as a decimal rounded to 4 decimal places when necessary. Locate each number on a real number line.

Question 4.
–$$\frac{199}{23}$$, -12.054, π3, $$\frac{\pi}{2}$$, $$\sqrt{200}$$, –$$\sqrt{289}$$

–$$\frac{199}{23}$$ = -8.65217
The real number above as a decimal rounded to 4 decimal places as -8.6522.
π3 = 31.00627
The real number above as a decimal rounded to 4 decimal places as 31.0063.
$$\frac{\pi}{2}$$ = 1.570796
The real number above as a decimal rounded to 4 decimal places as 1.5708.
$$\sqrt{200}$$ = 14.14213
The real number above as a decimal rounded to 4 decimal places as 14.1421.
–$$\sqrt{289}$$ = -17
Located each number on a real number line as we can observe in the above image.

### Math in Focus Course 2A Practice 1.4 Answer Key

Use a calculator. Compare each pair of real numbers using either < or >.

Question 1.
$$\sqrt{18}$$ and $$\sqrt{19}$$
$$\sqrt{18}$$ = 4.242
$$\sqrt{19}$$ = 4.358
$$\sqrt{18}$$ < $$\sqrt{19}$$
Explanation:
By using calculator the given real numbers are compared. The real number $$\sqrt{18}$$ is less than $$\sqrt{19}$$.

Question 2.
-2.23 and –$$\sqrt{5}$$
-2.23
–$$\sqrt{5}$$ = -2.24
-2.23 > –$$\sqrt{5}$$
Explanation:
By using calculator the given real numbers are compared. The real number -2.23 is greater than –$$\sqrt{5}$$.

Question 3.
6.61640 and $$\sqrt{38}$$
6.61640
$$\sqrt{38}$$ = 6.16441
6.61640 > $$\sqrt{38}$$
Explanation:
By using calculator the given real numbers are compared. The real number 6.61640 is greater than $$\sqrt{38}$$.

Question 4.
-87.09812 and -87.098126…
-87.09812 > -87.09813
Explanation:
By using calculator the given real numbers are compared. The real number -87.09812 is greater than -87.09813.

Use the irrational numbers below for questions 5 to 7.

Question 5.
Find the absolute value of each irrational number with 3 decimal places.
The absolute value of each irrational number with 3 decimal places are 5.099, 6.775, 3.142, 1.772.

Question 6.
Graph each irrational number on a real number line.

In the above image we can observe the given irrational numbers on a real number line.

Question 7.
Order the irrational numbers from greatest to least using the symbol >.
The irrational numbers from greatest to least are as below.

Use the real numbers below for questions 8 and 9.

Question 8.
Copy and complete the table using the real numbers above.

In the above table we can observe the given real number as rational numbers and irrational numbers.

Question 9.
Order the real numbers from least to greatest using the symbol <.
The real numbers from least to greatest are as below.

Solve.

Question 10.
Using a formula from physics, a sky diver knows that she can free fall $$\sqrt{875}$$ seconds before opening her parachute.
a) About how many seconds (to the nearest 0.01 second) can she free fall?
A skydiver knows she can free fall for $$\sqrt{875}$$ seconds before opening lier parachute.
$$\sqrt{875}$$ = 29.58 seconds
She can free fall for 29.58 seconds before opening her parachute.

b) For her next jump, she can free fall for 29.55 seconds. Does she have more time on her first or second jump? Explain using a number line.