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.
Answer:
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.
Answer:
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_________.
Answer:
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_______________.
Answer:
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 |
Answer:
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.
Answer:
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
Answer:
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
Answer:
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
Answer:
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
Answer:
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
Answer:
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____________.
Answer:
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 |
Answer:
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.
Answer:
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.
Answer:
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.
Answer:
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_____________.
Answer:
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_____________.
Answer:
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 |
Answer:
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.
Answer:
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.
Answer:
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.
Answer:
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.
Answer:
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.
Answer:
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.
Answer:
g.900.09.
Explanation:
In the above-given question,
given that,
(9 × 100) + (0 × 1) + (0 × 0.1) + (9 × 0.01)
900 + 0 + 0 + 0.09
900.09.