## Engage NY Eureka Math 4th Grade Module 6 Lesson 7 Answer Key

### Eureka Math Grade 4 Module 6 Lesson 7 Problem Set Answer Key

Question 1.
Write a decimal number sentence to identify the total value of the place value disks.

a.20.53.

Explanation:
In the above-given question,
given that,
2 tens + 5 tenths + 3 hundredths.
2 tens = 20.
5 tenths = 5/10.
5/10 = 0.5.
3 hundredths = 3/100.
3/100 = 0.03.
20 + 0.5 + 0.03 = 20.53.

b.20.53.

Explanation:
In the above-given question,
given that,
5 hundred + 4 hundredths.
5 hundred = 500.
4 hundredths = 4/100.
4/100 = 0.04.
500 + 0.04 = 500.04.

Question 2.
Use the place value chart to answer the following questions. Express the value of the digit in unit form

 hundreds tens ones . tenths hundredths 4 1 6 8 3

a. The digit ____4___ is in the hundreds place. It has a value of _______400________________.
b. The digit ___1____ is in the tens place. It has a value of _______10__________.
c. The digit ___8____ is in the tenths place. It has a value of ____0.8_____________.
d. The digit ____3___ is in the hundredths place. It has a value of ___0.03_________.

The digit 4 is in the hundreds place. It has a value of 400.
The digit 1 is in the tens place. It has a value of 10.
The digit 8 is in the tenths place. It has a value of 0.8.
The digit 3 is in the hundredths place. It has a value of 0.03.

Explanation:
In the above-given question,
given that,
The digit 4 is in the hundreds place. It has a value of 400.
4 x 100 = 400.
The digit 1 is in the tens place. It has a value of 10.
1 x 10 = 10.
The digit 8 is in the tenths place. It has a value of 0.8.
8/10 = 0.8.
The digit 3 is in the hundredths place. It has a value of 0.03.
3/100 = 0.03.

 hundreds tens ones . tenths hundredths 5 3 2 1 6

e. The digit __5_____ is in the hundreds place. It has a value of ______500___________.
f. The digit ___3____ is in the tens place. It has a value of _______30_______________.
g. The digit ___1____ is in the tenths place. It has a value of _______0.1______________.
h. The digit ___6____ is in the hundredths place. It has a value of ____0.6_______________.

The digit 5 is in the hundreds place. It has a value of 500.
The digit 3 is in the tens place. It has a value of 30.
The digit 1 is in the tenths place. It has a value of 0.1.
The digit 6 is in the hundredths place. It has a value of 0.06.

Explanation:
In the above-given question,
given that,
The digit 5 is in the hundreds place. It has a value of 500.
5 x 100 = 500.
The digit 3 is in the tens place. It has a value of 30.
3 x 10 = 30.
The digit 1 is in the tenths place. It has a value of 0.1.
1/10 = 0.1.
The digit 6 is in the hundredths place. It has a value of 0.06.
6/100 = 0.06.

Question 3.
Write each decimal as an equivalent fraction. Then, write each number in expanded form, using both decimal and fraction notation. The first one has been done for you.

 Decimal and Fraction Form Expanded Form Fraction Notation Decimal Notation 15.43 = 15$$\frac{43}{100}$$ (1 × 10) + (5 × 1) + (4 × $$\frac{1}{10}$$) + (3 × $$\frac{1}{100}$$) 10  +  5 +  $$\frac{4}{10}$$    + $$\frac{3}{100}$$ (1 × 10) + (5 × 1) + (4 × 0.1) + (3 × 0.01) 10 +  5 +  0.4   +   0.03 21.4 = 21$$\frac{4}{10}$$ (2 x 10) + (1 x 1) + (4 x $$\frac{1}{10}$$) 20 + 1 + $$\frac{4}{10}$$ ( 2 x 10) + (1 x 1) + (4 x 0.1) 20 + 1 + 0.4 38.09 = 38$$\frac{09}{100}$$ (3 × 10) + (8 × 1) + (0 × $$\frac{1}{10}$$) + (9 × $$\frac{1}{100}$$) 90  +  8 +  $$\frac{0}{10}$$    + $$\frac{9}{100}$$ (3 × 10) + (8 × 1) + (0 × 0.1) + (9 × 0.01) 30 +  8 +  0   +   0.09 50.2 = 50$$\frac{2}{10}$$ (5 × 10) + (0 × 1) + (2 × $$\frac{1}{10}$$) + (0 × $$\frac{1}{100}$$) 50  +  0 +  $$\frac{5}{10}$$    + $$\frac{0}{100}$$ (5 × 10) + (0 × 1) + (5 × 0.1) + (0 × 0.01) 50 +  0 +  0.5   +   0.01 301.07 = 301 $$\frac{07}{100}$$ (3 × 100) +  (1 × 1) + (3 × $$\frac{1}{100}$$) + (1 × $$\frac{1}{100}$$) 300  +  1 +  $$\frac{03}{10}$$    + $$\frac{1}{100}$$ (3 x 100) + ( 1 x 1) + ( 3 x 0.01) + (1 x 0.01) 300 + 1 + 0.03 + 0.01 620.80 = 620$$\frac{80}{100}$$ (6 × 100) + (2 × 10) + (8 × $$\frac{1}{100}$$) + (0 × $$\frac{1}{100}$$) 600  +  20 +  $$\frac{8}{10}$$    + $$\frac{0}{100}$$ (6 x 100) + ( 2 x 10) + ( 8 x 0.01) + (0 x 0.01) 600 + 20 + 0.08 + 0 800.08 = 800$$\frac{8}{100}$$ (8 × 100) + (0 × 1) + (0 × $$\frac{1}{10}$$) + (8 × $$\frac{1}{100}$$) 800  +  0 +  $$\frac{8}{10}$$    + $$\frac{0}{100}$$ (8 x 100) + ( 0 x 1) + ( 8 x 0.01) + (0 x 0.01) 800 + 0 + 0.08 + 0.01

a.15.43.

Explanation:
In the above-given question,
given that,
1 × 10) + (5 × 1) + (4 × 0.1) + (3 × 0.01)
10 +  5 +  0.4   +   0.03
15.43.

b.21.04.

Explanation:
In the above-given question,
given that,
( 2 x 10) + (1 x 1) + (4 x 0.1)
20 + 1 + 0.4

c.38.09.

Explanation:
In the above-given question,
given that,
(3 × 10) + (8 × 1) + (0 × 0.1) + (9 × 0.01)
30 +  8 +  0   +   0.09

d.50.2.

Explanation:
In the above-given question,
given that,
(5 × 10) + (0 × 1) + (5 × 0.1) + (0 × 0.01)
50 +  0 +  0.5   +   0.01

e.301.07.

Explanation:
In the above-given question,
given that,
(3 x 100) + ( 1 x 1) + ( 3 x 0.01) + (1 x 0.01)
300 + 1 + 0.03 + 0.01

f.620.80

Explanation:
In the above-given question,
given that,
(6 x 100) + ( 2 x 10) + ( 8 x 0.01) + (0 x 0.01)
600 + 20 + 0.08 + 0

g.800.08

Explanation:
In the above-given question,
given that,
(8 x 100) + ( 0 x 1) + ( 8 x 0.01) + (0 x 0.01)
800 + 0 + 0.08 + 0.01

### Eureka Math Grade 4 Module 6 Lesson 7 Exit Ticket Answer Key

Question 1.
Use the place value chart to answer the following questions. Express the value of the digit in unit form.

 hundreds tens ones . tenths hundredths 8 2 7 6 4

a. The digit ___8____ is in the hundreds place. It has a value of ________800___________.
b. The digit ___2____ is in the tens place. It has a value of _________20____________.
c. The digit ___6____ is in the tenths place. It has a value of ______0.6________________.
d. The digit ___4____ is in the hundredths place. It has a value of _____0.04____________.

The digit 8 is in the hundreds place. It has a value of 800.
The digit 2 is in the tens place. It has a value of 20.
The digit 6 is in the tenths place. It has a value of 0.6.
The digit 4 is in the hundredths place. It has a value of 0.04.

Explanation:
In the above-given question,
given that,
The digit 8 is in the hundreds place. It has a value of 800.
8 x 100 = 800.
The digit 2 is in the tens place. It has a value of 20.
2 x 10 = 20.
The digit 6 is in the tenths place. It has a value of 0.6.
6/10 = 0.6.
The digit 4 is in the hundredths place. It has a value of 0.04.
4/100 = 0.04.

Question 2.
Complete the following chart.

 Fraction Expanded Form Decimal Fraction Notation Decimal Notation 422$$\frac{8}{100}$$ (4× 100) + (2 × $$\frac{1}{10}$$) + (2 × $$\frac{1}{100}$$) (4 × 100) + (2 × 10) + (0 × 0.1) + (2 × 0.01) 400 +  20 +  0   +   0.02 420.02 39$$\frac{2}{100}$$ (3 × 100) + (9 × $$\frac{1}{10}$$) + (2 × $$\frac{1}{100}$$) (3 × 10) + (9 × 1) + (0 × 0.1) + (2 × 0.01) 30 +  9 +  0   +   0.02 39.02

a. 420.02.

Explanation:
In the above-given question,
given that,
(4× 100) + (2 × $$\frac{1}{10}$$) + (2 × $$\frac{1}{100}$$)
(4 × 100) + (2 × 10) + (0 × 0.1) + (2 × 0.01)
400 +  20 +  0   +   0.02
420.02.

b. 39.02.

Explanation:
In the above-given question,
given that,
(3 × 100) + (9 × $$\frac{1}{10}$$) + (2 × $$\frac{1}{100}$$)
(3 × 10) + (9 × 1) + (0 × 0.1) + (2 × 0.01)
30 +  9 +  0   +   0.02
39.02.

### Eureka Math Grade 4 Module 6 Lesson 7 Homework Answer Key

Question 1.
Write a decimal number sentence to identify the total value of the place value disks.

a.30.42.

Explanation:
In the above-given question,
given that,
3 tens + 4 tenths + 2 hundredths.
3 tens = 30.
4 tenths = 4/10.
4/10 = 0.4.
2 hundredths = 2/100.
2/100 = 0.02.
30 + 0.4 + 0.02 = 30.42.

b.400.03.

Explanation:
In the above-given question,
given that,
4 hundred + 3 hundredths.
4 hundred = 400.
3 hundredths = 3/100.
3/100 = 0.03.
400 + 0.03 = 400.03.

Question 2.
Use the place value chart to answer the following questions. Express the value of the digit in unit form.

 hundreds tens ones . tenths hundredths 8 2 7 6 4

a. The digit ___8____ is in the hundreds place. It has a value of _____800__________.
b. The digit ___2____ is in the tens place. It has a value of ________20______________.
c. The digit ___6____ is in the tenths place. It has a value of ______0.6_____________.
d. The digit ___4____ is in the hundredths place. It has a value of _____0.04_____________.

The digit 8 is in the hundreds place. It has a value of 800.
The digit 2 is in the tens place. It has a value of 20.
The digit 6 is in the tenths place. It has a value of 0.6.
The digit 4 is in the hundredths place. It has a value of 0.04.

Explanation:
In the above-given question,
given that,
The digit 8 is in the hundreds place. It has a value of 800.
8 x 100 = 800.
The digit 2 is in the tens place. It has a value of 20.
2 x 10 = 20.
The digit 6 is in the tenths place. It has a value of 0.6.
6/10 = 0.6.
The digit 4 is in the hundredths place. It has a value of 0.04.
4/100 = 0.04.

 hundreds tens ones . tenths hundredths 3 4 5 1 9

e. The digit ____3___ is in the hundreds place. It has a value of _______300______________.
f. The digit ___4____ is in the tens place. It has a value of _________40______________.
g. The digit ___1____ is in the tenths place. It has a value of ______0.1____________.
h. The digit ____9___ is in the hundredths place. It has a value of _____0.09_____________.

The digit 3 is in the hundreds place. It has a value of 300.
The digit 4 is in the tens place. It has a value of 40.
The digit 1 is in the tenths place. It has a value of 0.1.
The digit 9 is in the hundredths place. It has a value of 0.09.

Explanation:
In the above-given question,
given that,
The digit 3 is in the hundreds place. It has a value of 300.
3 x 100 = 300.
The digit 4 is in the tens place. It has a value of 40.
4 x 10 = 40.
The digit 1 is in the tenths place. It has a value of 0.1.
1/10 = 0.1.
The digit 9 is in the hundredths place. It has a value of 0.09.
9/100 = 0.09.

Question 3.
Write each decimal as an equivalent fraction. Then, write each number in expanded form, using both decimal and fraction notation. The first one has been done for you.

 Decimal and Fraction Form Expanded Form Fraction Notation Decimal Notation 14.23 = 14$$\frac{23}{100}$$ (1 × 10) + (4 × 1) + (2 × $$\frac{1}{10}$$) + (3 × $$\frac{1}{100}$$) 10 +  4 + $$\frac{2}{10}$$ + $$\frac{3}{100}$$ (1 × 10) + (4 × 1) + (2 × 0.1) + (3 × 0.01) 10 + 4   +   0.2    +    0.03 25.3 = 25$$\frac{3}{10}$$ (2 × 10) + (5 × 1) + (2 × $$\frac{1}{10}$$) + (5 × $$\frac{1}{100}$$) 20 +  5 + $$\frac{2}{10}$$ + $$\frac{5}{100}$$ (2 × 10) + (5 × 1) + (2 × 0.1) + (5 × 0.01) 20 + 5   +   0.2    +    0.05 39.07 = 39$$\frac{7}{100}$$ (3 × 10) + (9 × 1) + (0 × $$\frac{1}{10}$$) + (9 × $$\frac{1}{100}$$) 30 +  9 + $$\frac{0}{10}$$ + $$\frac{9}{100}$$ (3 × 10) + (9 × 1) + (3 × 0.1) + (9 × 0.01) 30 + 9  +   0.3    +    0.09 40.6 = 40$$\frac{6}{10}$$ (4 × 10) + (0 × 1) + (4 × $$\frac{1}{10}$$) + (0 × $$\frac{1}{100}$$) 40 +  0 + $$\frac{4}{10}$$ + $$\frac{0}{100}$$ (4 × 10) + (0 × 1) + (4 × 0.1) + (0 × 0.01) 40 + 0   +   0.4    +    0.00 208.90 = 208$$\frac{9}{10}$$ (2 × 100) + (8 × 1) + (2 × $$\frac{9}{10}$$) + ( 8× $$\frac{1}{100}$$) 200 +  8 + $$\frac{9}{10}$$ + $$\frac{8}{100}$$ (2 × 100) + (8 × 1) + (9 × 0.1) + (0 × 0.01) 200 + 8  +   0.9    +    0 510.07 = 510$$\frac{7}{100}$$ (5 × 100) + (1 × 10) + (0 × $$\frac{1}{10}$$) + (7 × $$\frac{1}{100}$$) 500 +  10 + $$\frac{0}{10}$$ + $$\frac{7}{100}$$ (5 × 100) + (1 × 10) + (0 × 0.1) + (7 × 0.01) 500 + 10  +   0   +    0.07 900.09 = 900$$\frac{9}{100}$$ (9 × 100) + (0 × 1) + (0 × $$\frac{1}{10}$$) + (9 × $$\frac{1}{100}$$) 900 +  0 + $$\frac{0}{10}$$ + $$\frac{9}{100}$$ (9 × 100) + (0 × 1) + (0 × 0.1) + (9 × 0.01) 900 + 0   +   0    +    0.09

a.14.23.

Explanation:
In the above-given question,
given that,
(1 × 10) + (4 × 1) + (2 × 0.1) + (3 × 0.01)
10 + 4   +   0.2    +    0.03
14.23.

b.25.3.

Explanation:
In the above-given question,
given that,
(2 × 10) + (5 × 1) + (2 × 0.1) + (5 × 0.01)
20 + 5   +   0.2    +    0.05
25.3.

c.39.07.

Explanation:
In the above-given question,
given that,
(3 × 10) + (9 × 1) + (3 × 0.1) + (9 × 0.01)
30 + 9  +   0.3    +    0.09
39.07.

d.49.6.

Explanation:
In the above-given question,
given that,
(4 × 10) + (0 × 1) + (4 × 0.1) + (0 × 0.01)
40 + 0   +   0.4    +    0.00
49.6.

e.208.90.

Explanation:
In the above-given question,
given that,
(2 × 100) + (8 × 1) + (9 × 0.1) + (0 × 0.01)
200 + 8  +   0.9    +    0
208.90.

f.510.07.

Explanation:
In the above-given question,
given that,
(5 × 100) + (1 × 10) + (0 × 0.1) + (7 × 0.01)
500 + 10  +   0   +    0.07
510.07.