Final answer:
The long division for 6÷5.04 is performed by first equalizing the decimal places of both numbers, then proceeding with the standard long division method. It's important to round the result to the same number of significant figures as the number with the least significant figures for accurate scientific calculations.
Step-by-step explanation:
To perform long division for the expression 6÷5.04, we first represent both numbers with the same number of decimal places. We can do this by multiplying 6 by 100 to get 600 and then divide by 5.04, converting the problem into 600÷5.04. Now, we can proceed with the long division process.
Here's how the process works step by step:
- Place 5.04 into the divisor's spot and 6.00 (or 600 after adjusting for decimal places) into the dividend's spot.
- Divide 5.04 into 6.00, which goes 1 time. Multiply 1 by 5.04 and subtract the result from 6.00.
- Bring down the next digit (which in this case would be a 0 since we are using placeholders for the original 6) and repeat the division and multiplication process.
- Continue this process, bringing down zeros and dividing until you either reach a remainder of 0 or have a sufficient number of decimal places.
In the context of scientific notation and significant figures, always adhere to the rule of rounding the result to the same number of digits as the number with the fewest significant figures, which is particularly relevant when working with measurements and precise calculations.