Envision Math 6th Grade Textbook Answer Key Topic 1.3 Exponents and Place Value

Exponents and Place Value

How can you write a number
using exponents?
Answer:
Each place in a place-value chart has a value that is 10 times as great as the place to its right. Use this pattern to write 1,000,000 as repeated multiplication.
Envision Math Grade 6 Answer Key Topic 1.3 Exponents and Place Value 1

Another Example
How do you write the expanded form of a number using exponents?
Answer:
Standard form: 562,384
Expanded form: (5 × 100,000) + (6 × 10,000) + (2 × 1,000) + (3 × 100) + (8 × 10) + 4
Expanded form
using exponents: (5 × 105) + (6 × 104) + (2 × 103) + (3 × 102) + (8 × 101 ) + (4 × 100)
Any number raised to the first power always equals that number. 101 = 10.

Explain It

Question 1.
How many times is 9 used as a factor in the exponent 98?
Answer:
8 times
Explanation:

Question 2.
Why does 3 × 100 = 3?
Answer:
100 = 1, so 3 × 100 = 3

Other Examples
Write each in exponential form.
100,000 = 105 10 × 10 × 10 = 103 1 trillion = 1012
Evaluate numbers in exponential form.
53 = 5 × 5 × 5 = 125 34 = 3 × 3 × 3 × 3 = 81

Envision Math Grade 6 Answer Key Topic 1.3 Exponents and Place Value 11
You can write the repeated multiplication of a number in exponential form.
Envision Math Grade 6 Answer Key Topic 1.3 Exponents and Place Value 2

Each place in the place-value chart can be written using an exponent.
Envision Math Grade 6 Answer Key Topic 1.3 Exponents and Place Value 3

Guided Practice

Do you know HOW?
Question 1.
Write 10,000 as repeated multiplication.
Answer:
10,000 = 10 × 10 × 10 × 10
Explanation:

Question 2.
Write 7 × 7 × 7 × 7 in exponential form.
Answer:
74
Explanation:

Question 3.
Write 37,169 in expanded form using exponents.
Answer:
(3 × 104) + (7 × 103) + (1 × 102) + (6 × 101) + (9 × 100)
Explanation:

Question 4.
Write 53 in standard form.
Answer:
125
Explanation:

Do you UNDERSTAND?
Question 5.
In the example at the top, why was the number 10 used as the base to write 1,000,000 in exponential form?
Answer:
See margin.
Explanation:

Question 6.
Using the example, how many times would 10 be repeatedly multiplied to equal 100,000?
Answer:
5 times. 100,000 = 10 × 10 × 10 × 10 × 10 = 10
Explanation:

Question 7.
How many zeros are in 107 when it is written in standard form?
Answer:
7
Explanation:

Independent Practice

Leveled Practice What number is the base?
Question 8.
49
Answer:
4
Explanation:

Question 9.
179
Answer:
17
Explanation:

What number is the exponent?
Question 10.
319
Answer:
9
Explanation:

Question 11.
2100
Answer:
100
Explanation:

Write each in exponential form.
Question 12.
1,000
Answer:
103
Explanation:

Question 13.
1,000,000,000
Answer:
109
Explanation:

Question 14.
10 × 10 × 10 × 10 × 10
Answer:
105
Explanation:

Write each number in expanded form using exponents.
Answer:
See margin
Explanation:

Question 15.
841
Answer:

Question 16.
5,832
Answer:

Question 17.
1,874,161
Answer:

Question 18.
22,600,000
Answer:

Evaluate 19 through 22.
Question 19.
62 = ☐
Answer:
36
Explanation:

Question 20.
104 = ☐
Answer:
10,000
Explanation:

Question 21.
43 = ☐
Answer:
64
Explanation:

Question 22.
27 = ☐
Answer:
128
Explanation:

Problem Solving

Question 23.
The population of one U.S. state is approximately 33,871,648. What is this number in expanded form using exponents?
Answer:
See margin
Explanation:

Question 24.
Reasoning What number raised to both the first power and the second power equals 1?
Answer:
1; 11 = 1 and 12 = 1
Explanation:

Question 25.
Writing to Explain Explain how to compare 24 and 42.
Answer:
24 = 2 × 2 × 2 × 2 = 16; 42 = 4 × 4 = 16; So 24 = 42.
Explanation:

Question 26.
In Exercise 23, what is the place of the digit 7?
A. hundreds
B. thousands
C. ten thousands
D. millions
Answer:
C. ten thousands
Explanation:

Question 27.
Writing to Explain Kalesha was asked to write 80,808 in expanded form using exponents. Her response was (8 × 102) + (8 × 101) + (8 × 100). Explain where she made mistakes and write the correct response.
Answer:
See margin
Explanation:

Question 28.
Think About the Process You invest $1 in a mutual fund. Every 8 years, your money doubles. If you don’t add more money, which expression shows how much your investment is worth after 48 years?
A. 1 48
B. 1 × 2 × 2 × 2 × 2 × 2
C. 1 + 2 + 2 + 2 + 2 + 2 + 2
D. 1 × 2 × 2 × 2 × 2 × 2 × 2
Answer:
Explanation:
D. 1 × 2 × 2 × 2 × 2 × 2 × 2

Question 29.
Number Sense Using the map, write the population of the United States in expanded form using exponents.
Envision Math Grade 6 Answer Key Topic 1.3 Exponents and Place Value 4
Answer:
See margin
Explanation:

Question 30.
In 1900, there were 76,803,887 people in the United States. How many more people were there in the United States in a recent year than in 1900?
Answer:
See margin
Explanation:

Algebra Connections

Solution Pairs
An equation is a mathematical sentence that uses an equals sign to show that two expressions are equal. Any values that make an equation true are solutions to the equation.

An inequality is a mathematical sentence that contains <, >, ≤, or ≥. Any value that makes the inequality true is a solution. You can graph the solutions of an inequality on a number line.

Example: Find two values for each variable that make the equation,
y = x + 3, true.
If x = 1, then y = 1 + 3 = 4 is true.
If x = 5, then y = 5 + 3 = 8 is true.
(1, 4) and (5, 8) are solution pairs.

Example: Graph three values that make the inequality, x > 3, true.
x = 3.1, x = 4, x = 5
Draw a number line. Plot three points that are greater than 3
Envision Math Grade 6 Answer Key Topic 1.3 Exponents and Place Value 5

For 1 through 4, copy the table and find two values for each variable that make the equation true.
Question 1.
y = 4 + x
Answer:
Envision Math Grade 6 Answer Key Topic 1.3 Exponents and Place Value 6
Explanation:

Question 2.
b = a – 2
Answer:
Envision Math Grade 6 Answer Key Topic 1.3 Exponents and Place Value 7
Explanation:

Question 3.
t = 3w
Answer:
Envision Math Grade 6 Answer Key Topic 1.3 Exponents and Place Value 8
Explanation:

Question 4.
y = x ÷ 2
Answer:
Envision Math Grade 6 Answer Key Topic 1.3 Exponents and Place Value 9
Explanation:

Question 5.
Copy the number line and graph 3 values that make the inequality, d ≥ 9, true.
Envision Math Grade 6 Answer Key Topic 1.3 Exponents and Place Value 10
Answer:
Any 3 points right of 9; or 9
Explanation:

Question 6.
Copy the number line and graph 3 values that make the inequality,\(\frac{x}{3}\) < 4, true.
Envision Math Grade 6 Answer Key Topic 1.3 Exponents and Place Value 10
Answer:
Any 3 points to left of 12
Explanation:

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