Question

lesson 3 homework 5•1
name brocky urauser date 4/8/26

1. use the place value chart and arrows to show how the value of each digit changes. the first one has been done for you.

a. 4.562 × 10 = 45.62
chart with digits 4,5,8,2 and arrows
b. 7.281 × 1000 =
empty place value chart
c. 8.254 × 1,000 =
empty place value chart

1. explain how and why the value of the 2 changed in (a), (b), and (c).
2. use the place value chart and arrows to show how the value of each digit changes. the first one has been done for you.

a. 3.48 ÷ 10 = 0.348
chart with digits 2,4,6 and arrows
b. 678 ÷ 100 =
empty place value chart
c. 87 ÷ 1,000 =
empty place value chart

1. explain how and why the value of the 5 changed in the quotients in (a), (b), and (c).

eureka math
lesson 3: reason concretely and pictorially using place value understanding to relate adjacent base ten units from millions to thousandths.

Explanation:

Step1: Solve 7.281 × 100

When multiplying by 100, shift digits 2 places right.
$7.281 \times 100 = 728.1$

Step2: Solve 9.254 × 1,000

When multiplying by 1000, shift digits 3 places right.
$9.254 \times 1000 = 9254$

Step3: Explain digit 2's value change (Q4)

• In (a): 2 is hundredths place ($0.02$).
• In (b): 2 shifts to ones place ($2$), 100× larger.
• In (c): 2 shifts to hundreds place ($200$), 10,000× larger than (a).

Multiplication by 10/100/1000 increases place value.

Step4: Solve 678 ÷ 100

When dividing by 100, shift digits 2 places left.
$678 \div 100 = 6.78$

Step5: Solve 67 ÷ 1,000

When dividing by 1000, shift digits 3 places left.
$67 \div 1000 = 0.067$

Step6: Explain digit 6's value change (Q2d)

• In (a): 6 is hundredths place ($0.06$).
• In (b): 6 is ones place ($6$), 100× larger than (a).
• In (c): 6 is hundredths place ($0.06$), 100× smaller than (b).

Division by 10/100/1000 decreases place value.

Answer:

Question 1:

b. $728.1$
c. $9254$

Question 4:

In part (a), the 2 represents 0.02 (hundredths place). In part (b), multiplying by 100 shifts the 2 to the ones place, making it worth 2 (100 times larger than in (a)). In part (c), multiplying by 1000 shifts the 2 to the hundreds place, making it worth 200 (10,000 times larger than in (a)). Multiplying by powers of 10 moves digits to higher place values, increasing their worth.

Question 2:

b. $6.78$
c. $0.067$
d. In part (a), the 6 represents 0.06 (hundredths place). In part (b), dividing 678 by 100 shifts the 6 to the ones place, making it worth 6 (100 times larger than in (a)). In part (c), dividing 67 by 1000 shifts the 6 to the hundredths place, making it worth 0.06 (100 times smaller than in (b)). Dividing by powers of 10 moves digits to lower place values, decreasing their worth.

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Place Value Charts (filled):

Question 1b:

Hundreds	Tens	Ones	.	Tenths	Hundredths	Thousandths

(Arrows shift 7.281 digits 2 places right)

Question 1c:

Thousands	Hundreds	Tens	Ones	.	Tenths

(Arrows shift 9.254 digits 3 places right)

Question 2b:

Tens	Ones	.	Tenths	Hundredths

(Arrows shift 678 digits 2 places left)

Question 2c:

Ones	.	Tenths	Hundredths	Thousandths

(Arrows shift 67 digits 3 places left)