What does ‘do not round intermediate calculations’ mean? Example: .3211
The correct answer and explanation is:
Correct Answer:
“Do not round intermediate calculations” means you should carry all decimal places through each step of a calculation and only round your final answer, not the numbers you get partway through.
Example:
Suppose you’re calculating: A=(5.327×0.3211)+1.25A = (5.327 \times 0.3211) + 1.25
- Multiply:
5.327×0.3211=1.7103797(Do not round this)5.327 \times 0.3211 = 1.7103797 \quad \text{(Do not round this)}
- Add:
1.7103797+1.25=2.96037971.7103797 + 1.25 = 2.9603797
- Now round the final answer as required, e.g., to two decimal places:
2.96\boxed{2.96}
300-Word Explanation:
In math and science, accuracy is very important. When solving problems with multiple steps, instructions will often say: “Do not round intermediate calculations.” This means you should not round off numbers between steps. You should only round after you have completed all the steps and are about to report the final answer.
Why is this important? Because rounding early can cause small errors to build up. Each time you round a number, you slightly change its value. Over several steps, those small changes can result in a final answer that is significantly incorrect, especially in more complex calculations like in chemistry, physics, or finance.
Let’s say you are calculating the area of a circle: A=πr2A = \pi r^2
If r=3.245r = 3.245, and you round it to 3.2 before squaring, you’ll get: 3.22=10.243.2^2 = 10.24
But if you use the full value: 3.2452=10.5290253.245^2 = 10.529025
That’s already a noticeable difference — and it gets even larger when you multiply by π\pi.
So, using the full precision (.3211 in your example) helps maintain accuracy until the end. Once you’re ready to write your final answer, then round it to the required number of decimal places (e.g., two decimal places, significant figures, etc.). This habit helps ensure your results are both accurate and acceptable in scientific and academic work.