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## Bridges in Mathematics Grade 5 Student Book Answer Key Unit 7 Module 3

**Bridges in Mathematics Grade 5 Student Book Unit 7 Module 3 Session 1 Answer Key **

**Exponents & Powers of Ten**

When you multiply 10s together, like 10 × 10 × 10, the product is called a power of 10. You can use an exponent to show a power of 10. The exponent tells how many times to multiply 10 by itself.

Question 1.

Complete the chart below to show different powers of 10.

Answer:

The power of 10 can be calculated by counting the number of times 10 is multiplying by itself.

Question 2.

Multiply each whole number by powers of 10, using the steps shown in the example.

ex: 43 × 10^{2} = 43 × (10 × 10) = 43 × 100 = 4,300

a. 79 × 10^{3} = _________________

Answer:

79 × (10 × 10 × 10)

79 × 1000

79000

b. 105 × 10^{2} = _________________

Answer:

105 × (10 × 10)

105 × 100

10500

c. 4568 × 10^{4} = ________________

Answer:

4568 × (10 × 10 × 10 × 10)

4568 × 10000

45680000

d. 17 × 10^{5} = ________________

Answer:

17 × (10 × 10 × 10 × 10 × 10)

17 × 100000

1700000

Question 3.

Multiply each decimal by powers of 10, using the steps shown in the example.

ex 5.8 × 10^{3} = 5.8 × (10 × 10 × 10) = 5.8 × 1,000 = 5,800

a. 4.7 × 10^{3} = _________________

Answer:

4.7 × (10 × 10 × 10)

4.7 × 1000

4700

b. 0.68 × 10^{2} = ________________

Answer:

0.68 × (10 × 10)

0.68 × 100

68

c. 5.16 × 10^{4} = ________________

Answer:

5.16 × (10 × 10 × 10 × 10)

5.16 × 10000

51600

d. 12.63 × 10^{5} = ________________

Answer:

12.63 × (10 × 10 × 10 × 10 × 10)

12.63 × 100000

1263000

**Bridges in Mathematics Grade 5 Student Book Unit 7 Module 3 Session 2 Answer Key **

**Patterns in Multiplying by Powers of Ten**

Question 1.

The post office sells 14 stamps. Fill out the table below to show how much it would cost to buy different quantities of 1¢ stamps.

a. What do you notice about multiplying by 0.01?

Answer:

Question 2.

Amelia feeds her pet lizard crickets. The pet store sells crickets for 104 each. Fill out the table below to show how much it would cost to buy different quantities of crickets.

a. What do you notice about multiplying by 0.10?

Answer:

Question 3.

Alfonso’s company sells T-shirts to soccer teams. Each T-shirt costs $10. Fill out the table below to show how much it would cost to buy different quantities of T-shirts.

a. What do you notice about multiplying by 10?

Answer:

**Multiplying by Powers of Ten Practice**

106 × 0.01 = _______________

47 × 0.01 = _______________

3 × 0.01 = _______________

0.6 × 0.01 = _______________

0.32 × 0.01 = _______________

0.1 × 0.01 = _______________

10 × 0.01 = _______________

452 × 0.1 = _______________

302 × 0.1 = _______________

64 × 0.1 = _______________

0.9 × 0.1 = _______________

0.57 × 0.1 = _______________

0.04 × 0.1 = _______________

0.1 × 0.1 = _______________

360 × 10 = _______________

23 × 10 = _______________

4 × 10 = _______________

0.7 × 10 = _______________

0.54 × 10 = _______________

0.01 × 10 = _______________

0.32 × 100 = _______________

4.3 × 100 = _______________

4 × 100 = _______________

45 × 100 = _______________

309 × 100 = _______________

0.1 × 100 = _______________

0.17 × 1,000 = _______________

0.34 × 1,000 = _______________

9.6 × 1,000 = _______________

603 × 1,000 = _______________

0.01 × 1,000 = _______________

Answer:

106 × 0.01 = 106 × \(\frac{1}{100}\) = 1.06

47 × 0.01 = 47 × \(\frac{1}{100}\) = 0.47

3 × 0.01 = 3 × \(\frac{1}{100}\) = 0.03

0.6 × 0.01 = 6 × \(\frac{1}{10}\) × \(\frac{1}{100}\) = 0.006

0.32 × 0.01 = 32 × \(\frac{1}{100}\) × \(\frac{1}{100}\) = \(\frac{32}{10000}\) = 0.0032

0.1 × 0.01 = 1 × \(\frac{1}{10}\) × \(\frac{1}{100}\) = 0.001

10 × 0.01 = 10 × \(\frac{1}{100}\) = \(\frac{1}{10}\) = 0.1

452 × 0.1 = 452 × \(\frac{1}{10}\) = 45.2

302 × 0.1 = 302 × \(\frac{1}{10}\) = 30.2

64 × 0.1 = 64 × \(\frac{1}{10}\) = 6.4

0.9 × 0.1 = 9 × \(\frac{1}{10}\) × \(\frac{1}{10}\) = 0.09

0.57 × 0.1 = 57 × \(\frac{1}{100}\) × \(\frac{1}{10}\) = 57 × \(\frac{1}{1000}\) = 0.057

0.04 × 0.1 = 4 × \(\frac{1}{100}\) × \(\frac{1}{10}\) = 4 × \(\frac{1}{1000}\) = 0.004

0.1 × 0.1 = \(\frac{1}{10}\) × \(\frac{1}{10}\) = 0.01

360 × 10 = 3600

23 × 10 = 230

4 × 10 = 40

0.7 × 10 = 7 × \(\frac{1}{10}\) × 10 = 7

0.54 × 10 = 54 × \(\frac{1}{100}\) × 10 = 5.4

0.01 × 10 = 1 × \(\frac{1}{100}\) × 10 = 0.1

0.32 × 100 = 32 × \(\frac{1}{100}\) × 100 = 32

4.3 × 100 = 43 × \(\frac{1}{10}\) × 100 = 430

4 × 100 = 400

45 × 100 = 4500

309 × 100 = 30900

0.1 × 100 = 1 × \(\frac{1}{10}\) × 100 = 10

0.17 × 1,000 = 17 × \(\frac{1}{100}\) × 1000 = 170

0.34 × 1,000 = 34 × \(\frac{1}{100}\) × 1000 = 340

9.6 × 1,000 = 96 × \(\frac{1}{10}\) × 1000 = 9600

603 × 1,000 = 603,000

0.01 × 1,000 = 1 × \(\frac{1}{100}\) × 1000 = 10

**More Exponents & Powers of Ten**

Question 1.

Multiply each number by powers of 10, using the steps shown in the example.

ex: 29 × 10^{3} = 29 × (10 × 10 × 10) = 29 × 1,000 = 29,000

ex: 7.2 × 10^{3} = 7.2 × (10 × 10 × 10) = 7.2 × 1,000 = 7,200

a. 62 × 10^{3} = _______________

Answer:

62 × (10 × 10 × 10)

62 × 1000

62000

b. 2,078 × 10^{2} = _______________

Answer:

2078 × (10 × 10)

2078 × 100

207,800

c. 47 × 10^{4} = _______________

Answer:

47 × (10 × 10 × 10 × 10)

47 × 10000

470000

d. 6.8 × 10^{3} = _______________

Answer:

6.8 × (10 × 10 × 10)

6.8 × 1000

6800

e 0.098 × 10^{3} = _______________

Answer:

0.098 × (10 × 10 × 10)

98

f. 26.75 × 10^{4} = _______________

Answer:

26.75 × (10 × 10 × 10 × 10)

26.75 × 10000

267500

Question 2.

Sara solved the problems below, and got all the answers correct.

76 × 10^{1} = 76

76 × 10^{2} = 7,600

76 × 10^{3} = 76,000

76 × 10^{4} = 760,000

a. Describe what is happening to the number of zeros in these problems.

Answer:

The number of zeros in these problems is incraesing.

b. Explain why it works that way.

Answer:

As the power of 10 is increasing, the number of zeroes are increasing.

In 2012, the estimated population of Chicago, Illinois, was 2,714,856. The chart below shows four different ways to write this number.

Question 3.

Use the information shown above to help write the 2012 estimated population of Los Angeles, California, in word, expanded, and exponential form. (The standard form is written in for you.)

Answer:

**Bridges in Mathematics Grade 5 Student Book Unit 7 Module 3 Session 3 Answer Key **

**Patterns in Dividing by Powers of Ten**

Question 1.

Alfonso’s company sells T-shirts to soccer teams. Each T-shirt costs $10.

a. If you spent $1,030, how many shirts could you buy?

Answer:

Given that Alfonso’s company sells T-shirts to soccer teams costing $10.

If $1,030 is spent, 1030÷10 = 103

103 shirts can be bought.

b. Fill out the table below to show how many T-shirts you could buy with different amounts of money.

Answer:

c. What do you notice about dividing by 10?

Answer:

Dividing by 10 will decrease the number.

Question 2.

Amelia feeds her pet lizard crickets. The pet store sells crickets for 10¢ each.

a. If Amelia spent $1.30 on crickets last week, how many crickets did she buy?

Answer:

Given that the pet store sells crickets for 10¢ each and Amelia spent $1.30 on crickets last week.

1 dollar equals 100 cents. 10¢ will be equal to $0.1

To calculate the number of crickets, divide 1.30 by 0.1 which will be 13

Thus, she will buy 13 crickets.

b. Fill out the table below to show how much it would cost to buy different quantities of crickets.

Answer:

c. What do you notice about dividing by 0.10?

Answer:

Dividing by 0.10 will increase the number value.

Question 3.

The post office sells 14 stamps.

a. If you spent $2.08, how many 14 stamps could you buy?

Answer:

Given that the post office sells 14 stamps.

If $2.08 is spent, 2.08÷0.01 = 208 stamps can be bought.

b. Fill out the table below to show how many stamps you could buy with different amounts of money.

Answer:

c. What do you notice about dividing by 0.01?

Answer:

Dividing by 0.10 will increase the numbers.

**Dividing by Powers of Ten Practice**

**Complete the following equations.**

3000 ÷ 1000 = ______________

2504 ÷ 1000 = ______________

372 ÷ 1000 = ______________

0.6 ÷ 1000 = ______________

0.03 ÷ 1000 = ______________

900 ÷ 100 = ______________

406 ÷ 100 = ______________

7 ÷ 100 = ______________

3.2 ÷ 100 = ______________

0.08 ÷ 100 = ______________

405 ÷ 10 = ______________

0.63 ÷ 10 = ______________

87 ÷ 0.1 = ______________

6 ÷ 0.1 = ______________

0.5 ÷ 0.1 = ______________

0.48 ÷ 0.1 = ______________

3 ÷ 0.01 = ______________

6.9 ÷ 0.01 = ______________

0.8 ÷ 0.01 = ______________

409 ÷ 0.01 = ______________

Answer:

3000 ÷ 1000 = 3

2504 ÷ 1000 = 2.504

372 ÷ 1000 = 0.372

0.6 ÷ 1000 = 0.0006

0.03 ÷ 1000 = 0.00003

900 ÷ 100 = 9

406 ÷ 100 = 4.06

7 ÷ 100 = 0.07

3.2 ÷ 100 = 0.032

0.08 ÷ 100 = 0.0008

405 ÷ 10 = 40.5

0.63 ÷ 10 = 0.063

87 ÷ 0.1 = 870

6 ÷ 0.1 = 60

0.5 ÷ 0.1 = 5

0.48 ÷ 0.1 = 4.8

3 ÷ 0.01 = 300

6.9 ÷ 0.01 = 690

0.8 ÷ 0.01 = 80

409 ÷ 0.01 = 40900

**Multiplying & Dividing by Powers of Ten**

Question 1.

Solve the multiplication problems below.

34 × 0.01 = ______________

34 × 0.10 = ______________

34 × 1 = ______________

34 × 10 = ______________

34 × 100 = ______________

34 × 1,000 = ______________

Answer:

34 × 0.01 = 0.34

34 × 0.10 = 3.4

34 × 1 = 34

34 × 10 = 340

34 × 100 = 3400

34 × 1,000 = 34,000

Question 2.

Solve the division problems below.

34 ÷ 0.01 = ______________

34 ÷ 0.10 = ______________

34 ÷ 1 = ______________

34 ÷ 10 = ______________

34 ÷ 100 = ______________

34 ÷ 1,000 = ______________

Answer:

34 ÷ 0.01 = 3400

34 ÷ 0.10 = 340

34 ÷ 1 = 34

34 ÷ 10 = 3.4

34 ÷ 100 = 0.34

34 ÷ 1,000 = 0.034

Question 3.

What patterns do you notice in the equations you completed above?

Answer:

When two numbers are multiplied, the result will be more in value.

When two numbers are divided, the result will be less than the numbers.

Question 4.

Solve the multiplication and division problems below.

62 ÷ 100 = ______________

3.4 × 1000 = ______________

7.89 ÷ 0.10 = ______________

0.43 × 100 = ______________

0.08 × 0.01 = ______________

123.05 ÷ 100 = ______________

Answer:

62 ÷ 100 = 0.62

3.4 × 1000 = 3400

7.89 ÷ 0.10 = 789

0.43 × 100 = 43

0.08 × 0.01 = 0.0008

123.05 ÷ 100 = 12305

Question 5.

Ramon bought erasers shaped like animals to give away at Family Night at his school. Each eraser costs $0.10. If he spent $25.60, how many erasers did he buy?

a. Write a division equation to represent this situation.

Answer:

The division equation to represent this situation will be 25.60 ÷ 0.10

b. Solve the problem using a strategy that makes sense to you. Show all your work.

Answer:

25.60 ÷ 0.10

25.60 ÷ \(\frac{1}{10}\)

25.60 × 10

256

**Bridges in Mathematics Grade 5 Student Book Unit 7 Module 3 Session 4 Answer Key **

**Using the Area Model to Multiply Decimal Numbers**

Question 1.

A piece of paper measures 0.3 m by 0.65 m.

a. Estimate the total area of the piece of paper.

Answer:

Given that a piece of paper measures 0.3 m by 0.65 m.

The total area of the piece of paper will be 0.3 × 0.6= 0.18 sq.m

b. Make a labeled sketch of the piece of paper and use it to calculate an exact answer.

Answer:

The total area of the piece of paper will be 0.3 × 0.65 = 0.195 sq.m

Question 2.

The city park measures 1.2 km by 0.63 km.

a. Estimate the total area of the park.

Answer:

Given that the city park measures 1.2 km by 0.63 km.

The estimated area wii be 1 × 0.6 = 0.6 sq.km

b. Make a labeled sketch of the park and use it to calculate an exact answer.

Answer:

The exact answer will be 0.63 × 1.2 = 0.756 sq.km

Question 3.

Use an algorithm or sketch arrays to find the products below.

Answer:

Step 1: Initially, ignore the decimal point and multiply the two numbers normally.

Step 2: After multiplication, count the number of decimal places in the decimal number. The product obtained after multiplication will have the same number of decimal places.

Step 3: Place the decimal point in the obtained product.

**Multiplying Two Decimal Numbers**

Question 1.

The memory card for Steve’s camera measures 0.82 inches by 1.25 inches.

a. What do you estimate the total area of the memory card is?

Answer:

Given that the memory card for Steve’s camera measures 0.82 inches by 1.25 inches.

The estimated area of the memory card will be 0.8 × 1.2 = 0.96 sq.in

b. Find the exact area of the memory card. Show all your work. Fill in the array below if it helps you.

Answer:

Multiply the numbers to get the area of respective rectangles.

Add the obtained areas to get the complete area.

c. What is the place value of the smallest unit of area in the array above?

Answer:

The smallest unit of area is 0.001

The place value will be thousandths.

Question 2.

Fill in an estimate and the exact answer for the problems below. Show your work.

Estimate:

Exact Answer: ____________

Answer:

The estimated product will be 0.4 × 0.5 = 0.2

The actual answer will be 0.2240

Estimate:

Exact Answer: ____________

The estimated product will be 2 × 1 = 2

The exact product will be 2.06 × 1.42 = 2.9252

Estimate:

Exact Answer: ____________

The estimated product will be 3 × 0 = 0

The exact product will be 1.036