the teacher said something about doing the correct sig figs..im not sure if it applies to this, im so confused!
10.2* 7.5 =76.5?
27.1/5.31 =5.103578154425612??
2.712 + 10.8= 13.512?
The first to the correct number of sig digits (determined by 7.5, the least precise number) will be 77
The second should be to three sig digits, 5.10
The third should be precise to the tenths digit, (determined by 10.8, the least precise number),or 13.5
http://www.fordhamprep.org/gcurran/sho/sho/lessons/lesson23.htm
I can help you understand how to determine the correct number of significant figures (sig figs) in a calculation.
Sig figs are used to indicate the level of precision in a measurement or calculation. They tell us how certain or uncertain the final result is. When performing calculations, it's important to consider sig fig rules to ensure accuracy.
Sig Fig Rule 1: Non-Zero Digits
Non-zero digits are always significant. In your first example, 10.2 and 7.5 are both non-zero digits, so they are significant.
Sig Fig Rule 2: Leading Zeros
Leading zeros, or zeros that come before any non-zero digits, are not significant. In your first example, there are no leading zeros.
Sig Fig Rule 3: Captive Zeros
Captive zeros, or zeros between non-zero digits, are always significant. In your first example, there are no captive zeros.
Sig Fig Rule 4: Trailing Zeros
Trailing zeros, or zeros to the right of the non-zero digits and the decimal point, are only significant if there is a decimal point present. In your first example, there is no decimal point, so the trailing zero in 10.2 is not significant.
Now, let's apply these rules to your calculations:
1) 10.2 * 7.5 = 76.5
In this calculation, both 10.2 and 7.5 have three significant figures. Since multiplication involves multiplying the number of significant figures, the result should have three significant figures as well. Therefore, the correct answer is 76.5.
2) 27.1 / 5.31 = 5.103578154425612
In this division calculation, 27.1 has three significant figures, and 5.31 has four significant figures. When dividing, you should consider the least number of significant figures. So the result should only have three significant figures. In this case, you rounded it correctly to 5.103.
3) 2.712 + 10.8 = 13.512
In this addition calculation, the number of decimal places in each term is important.
2.712 has four decimal places, while 10.8 has one decimal place.
When adding or subtracting, you should round the result to the least number of decimal places. So the answer should have one decimal place. In this case, you rounded it correctly to 13.5.
By following these rules, you can determine the correct number of significant figures in your calculations. Remember to be mindful of the decimal point and follow the appropriate rounding procedures.