MULTIPLYING AND DIVIDING BY 10 100 AND 1000

Complete the following table.

Problem 1 :

a, Multiply  607 by 1000

b. Multiply 607 by 10

c. Divide 607 by 100

Solution :

a.

607 × 1000

Since there is no decimal point in 607, we have to assume that there is decimal point at the end.

We multiply by 1000. So, we have to move the decimal point three digits to the right.

607 × 1000 = 607000

b.

607 × 10

Since there is no decimal point in 607, we have to assume that there is decimal point at the end.

We divided by 10. So, we have to move the decimal point one digit to the left.

607 × 10 = 6070

c.

607 ÷ 100

Since there is no decimal point in 607, we have to assume that there is decimal point at the end.

We divided by 100. So, we have to move the decimal point two digits to the left.

607 ÷ 100 = 6.07

Problem 2 :

a, Multiply  4.901 by 1000

b. Multiply 4.901 by 10

c. Divide 4.901 by 100

Solution :

a.

4.901 × 1000

Decimal point shifted to the right by one place since 1000 has three zeros.

= 4901

b.

4.901 × 10

Decimal point shifted to the right by one place since 10 has one zero.

= 49.01

c.

4.901 ÷ 100

Since 4.901 is divided by 100, decimal point has to be shifted two digits to the right.

4.901 ÷ 100 = 0.04901

Problem 3 :

a. Multiply  0.08 by 1000

b. Multiply 0.08 by 10

c. Divide 0.08 by 100

Solution :

a.

0.08 × 1000

Decimal point shifted to the right by one place since 1000 has three zeros.

0.08 × 1000 = 80

b.

0.08 × 10

Decimal point shifted to the right by one place since 10 has one zero.

0.08 × 10 = 0.8

c.

0.08 ÷ 100

Since 0.08 is divided by 100, decimal point has to be shifted two digits to the right.

0.08 ÷ 100 = 0.0008

Problem 4 :

a. Multiply  17.809 by 1000

b. Multiply 17.809 by 10

c. Divide 17.809 by 100

Solution :

a.

17.809 × 1000

Decimal point shifted to the right by one place since 1000 has three zeros.

17.809 × 1000 = 17809

b.

17.809 × 10

Decimal point shifted to the right by one place since 10 has one zero.

17.809 × 10 = 178090

c.

17.809 ÷ 100

Since 17.809 is divided by 100, move the decimal point two digits to the left.

17.809 ÷ 100 = 0.17809

Problem 5 :

a. Multiply  37 by 1000

b. Multiply 37 by 10

c. Divide 37 by 100

Solution :

a.

37 × 1000

Since there is no decimal point in 37, we have to assume that there is decimal point at the end.

We multiply by 1000. So, we have to move the decimal point three digits to the right.

37 × 1000 = 37000

b.

37 × 10

Since there is no decimal point in 37, we have to assume that there is decimal point at the end.

We divided by 10. So, we have to move the decimal point one digit to the right.

37 × 10 = 370

c.

37 ÷ 100

Since there is no decimal point in 37, we have to assume that there is decimal point at the end.

We divided by 100. So, we have to move the decimal point two digits to the left.

37 ÷ 100 = 0.37

Dividing by 10, 100 and 1000.

Divide the following numbers by 10,100 and 1000 to complete the table.

Problem 1 :

a. Divide 56.9 by 10

b. Divide 56.9 by 100

c. Divide 56.9 by 1000

Solution :

a.

56.9 ÷ 10

Since 56.9 is divided by 10, move the decimal point one digit to the left.

56.9 ÷ 10 = 5.69

b.

56.9 ÷ 100

Since 56.9 is divided by 100, move the decimal point two digits to the left.

56.9 ÷ 100 = 0.569

c.

56.9 ÷ 1000

Since 56.9 is divided by 1000, move the decimal point three digits to the left.

56.9 ÷ 1000 = 0.0569

Problem 2 :

a. Divide 209 by 10

b. Divide 209 by 100

c. Divide 209 by 1000

Solution :

a.

209 ÷ 10

Since there is no decimal point in 209, we have to assume that there is decimal point at the end.

We divided by 10. So, we have to move the decimal point one digit to the left.

209 ÷ 10 = 20.9

b.

209 ÷ 100

Since there is no decimal point in 209, we have to assume that there is decimal point at the end.

We divided by 100. So, we have to move the decimal point two digits to the left.

209 ÷ 100 = 2.09

c.

209 ÷ 1000

Since there is no decimal point in 209, we have to assume that there is decimal point at the end.

We divided by 100. So, we have to move the decimal point three digits to the left.

209 ÷ 1000 = 0.209

Problem 3 :

a, Divide 4.56 by 10

b. Divide 4.56 by 100

c. Divide 4.56 by 1000

Solution :

a.

4.56 ÷ 10

Since 4.56 is divided by 10, decimal point has to be shifted one digit to the left.

4.56 ÷ 10 = 0.456

b.

4.56 ÷ 100

Since 4.56 is divided by 10, decimal point has to be shifted two digits to the left.

4.56 ÷ 100 = 0.0456

c.

4.56 ÷ 1000

Since 4.56 is divided by 10, decimal point has to be shifted three digits to the left.

4.56 ÷ 1000 = 0.00456

Problem 4 :

a, Divide 709.6 by 10

b. Divide 709.6 by 100

c. Divide 709.6 by 1000

Solution :

a.

709.6 ÷ 10

Since 709.6 is divided by 10, move the decimal point one digit to the left.

709.6 ÷ 10 = 70.96

b.

709.6 ÷ 100

Since 709.6 is divided by 100, move the decimal point two digits to the left.

709.6 ÷ 100 = 7.096

c.

709.6 ÷ 1000

Since 709.6 is divided by 1000, move the decimal point three digits to the left.

709.6 ÷ 1000 = 0.7096

Problem 5 :

a, Divide 0.072 by 10

b. Divide 0.072 by 100

c. Divide 0.072 by 1000

Solution :

a.

0.072 ÷ 10

Since 0.072 is divided by 10, decimal point has to be shifted one digit to the left.

0.072 ÷ 10 = 0.0072

b.

0.072 ÷ 100

Since 0.072 is divided by 100, decimal point has to be shifted two digits to the left.

0.072 ÷ 100 = 0.00072

c.

0.072 ÷ 1000

Since 0.072 is divided by 1000, decimal point has to be shifted three digits to the left.

0.072 ÷ 1000 = 0.000072