6893.5 × 603.3 × 0.3019 is equal in value to:

Given:

Expression: 6893.5 × 603.3 × 0.3019

Formula used:

For two products to be equal, the overall decimal place shifts must balance out.

Calculations:

Original expression's decimal shifts (relative to integer):

6893.5 (1 place left) × 603.3 (1 place left) × 0.3019 (4 places left)

Total left shift = 1 + 1 + 4 = 6 places.

Let's examine the options for a total 6-place left shift:

Option 1: 6.8935 (4 left) × 60.33 (2 left) × 30.19 (2 right)

Net shift = 4 + 2 - 2 = 4 places left. (Incorrect)

Option 2: 6.8935 (4 left) × 6.033 (3 left) × 301.9 (1 right)

Net shift = 4 + 3 - 1 = 6 places left. (Correct)

Wait, let me re-evaluate the shifts from the original numbers, not relative to integers. This is about comparing the original product to the product of the options.

Let P = 6893.5 × 603.3 × 0.3019

Option 1: 6.8935 × 60.33 × 30.19

(6893.5 / 1000) × (603.3 / 10) × (0.3019 × 100)

= P × (1/1000) × (1/10) × 100 = P × (100/10000) = P / 100 (Incorrect)

Option 2: 6.8935 × 6.033 × 301.9

(6893.5 / 1000) × (603.3 / 100) × (0.3019 × 1000)

= P × (1/1000) × (1/100) × 1000 = P × (1000/100000) = P / 100 (Incorrect)

Option 3: 68.935 × 6033 × 3.019

(6893.5 / 100) × (603.3 × 10) × (0.3019 × 10)

= P × (1/100) × 10 × 10 = P × (100/100) = P × 1 (Correct)

Option 4: 689.35 × 603.3 × 301.9

(6893.5 / 10) × 603.3 × (0.3019 × 1000)

= P × (1/10) × 1 × 1000 = P × (1000/10) = P × 100 (Incorrect)

∴ The correct answer is option 3.

Alternate Method 

Given:

Expression: 6893.5 × 603.3 × 0.3019

Formula used:

When we shift the decimal point in all numbers such that the overall scaling factor remains 1, the product stays the same.

Calculation:

Original numbers:

6893.5 = 68.935 × 100

603.3 = 6033 ÷ 10

0.3019 = 3.019 ÷ 10

Let's adjust them oppositely to balance the product:

6893.5 ÷ 100 = 68.935   \(\rightarrow\) ÷100

603.3 × 10 = 6033   \(\rightarrow\) ×10

0.3019 × 10 = 3.019   \(\rightarrow\) ×10

Overall scaling factor:

⇒ (÷100) × (×10) × (×10) = ÷100 × 100 = 1

Therefore, the product remains the same.

∴ The correct answer is option (3): 68.935 × 6033 × 3.019.