How do i Find the product. 67.8 x 0.45 *
The Correct Answer and Explanation is:
To find the product of 67.8 × 0.45, you multiply the two numbers together:67.8×0.45=30.5167.8 \times 0.45 = 30.5167.8×0.45=30.51
Detailed Explanation
To solve the multiplication problem 67.8 × 0.45, it’s important to understand both how multiplication works with decimals and why the answer is what it is.
Step-by-Step:
- Ignore the decimals temporarily.
First, remove the decimal points to simplify the multiplication.- 67.8 becomes 678 (moved the decimal 1 place to the right).
- 0.45 becomes 45 (moved the decimal 2 places to the right).
- Multiply the whole numbers.
Now multiply 678 × 45: 678×45=30,510678 \times 45 = 30,510678×45=30,510 - Count the total number of decimal places.
- 67.8 had 1 decimal place.
- 0.45 had 2 decimal places.
- So, the product must have 1 + 2 = 3 decimal places.
- Place the decimal point in the product.
Take the result from step 2 (30,510) and move the decimal point 3 places from the right: 30,510→30.51030,510 \rightarrow 30.51030,510→30.510 So, the final answer is: 30.51\boxed{30.51}30.51
Why This Method Works:
Multiplication with decimals follows the same basic rules as whole number multiplication. The key difference is how we handle place value. When we multiply decimals, we treat the numbers as if they were whole numbers and adjust for the decimals at the end. This adjustment ensures that the size and scale of the numbers remain accurate.
Understanding place value is crucial. Multiplying by 0.45 means taking less than half of 67.8, so it makes sense that the result (30.51) is smaller than the original number.
Thus, the product of 67.8 × 0.45 is 30.51.
