Question

1. Write the following in exponential form and as a multiplication sentence using only 10 as a factor

Answer 1

Answer:

1. a. 1,000 = 10³ = 10 × 10 × 10

b. 100 × 100 = 10² × 10² = 10 × 10 × 10 × 10

2. a. 3 × 10² = 300

b. 2.16 × 10⁴ = 21,600

c. 800 ÷ 10³ = 0.8

d. 754.2 ÷ 10² = 7.542

Step-by-step explanation:

3. a. 1,000

There are 3 zeros in 1000. This is equivalent to 10 raised to the power of 3. Writing this in multiplication sentence using 19 as the only factor, we would have:

1,000 = 10³ = 10 × 10 × 10

b. 100 × 100

Using the same logic as explained in (a) above, we would have:

100 × 100 = 10² × 10² = 10 × 10 × 10 × 10

2. a. 3 × 10²

Convert 10² to 100 and multiply both numbers

3 × 10² = 3 × 10 × 10 = 3 × 100 = 300

b. 2.16 × 10⁴

2.16 × 10 × 10 × 10 × 10 = 2.16 × 10,000

Multiplying both numbers, since we have 4 zeros, move the decimal point 4 places to the right.

2.16 × 10,000 = 21,600

c. 800 ÷ 10³ = 800 ÷ 10 × 10 × 10

800 ÷ 1,000

There are 3 zeros in 1000, since we are dividing, move the decimal point 3 places to the left.

800 ÷ 1,000 = 0.8

d. 754.2 ÷ 10² = 754.2 ÷ 10 × 10

754.2 ÷ 100

Move the decimal point 2 places to the left.

754.2 ÷ 100 = 7.542