Any help would be appreciated!
What is 38.896/5.1 + 509.15 to the correct number of significant figures?
516.78
What is (154+8446.1)/54 to the correct number of significant figures?
159.261
Thanks!
Rules for counting significant figures are summarized below.
Zeros within a number are always significant. Both 4308 and 40.05 contain four significant figures.
Zeros that do nothing but set the decimal point are not significant. Thus, 470,000 has two significant figures.
Trailing zeros that aren't needed to hold the decimal point are significant. For example, 4.00 has three significant figures.
I understand that, but this is different because it's a complex number.
You're welcome! I'm glad I can help.
To determine the correct number of significant figures in a mathematical expression, you need to consider the significant figures in each individual number involved.
For the first expression: 38.896/5.1 + 509.15
The division of 38.896 by 5.1 produces 7.59843137. Since 5.1 has two significant figures, the result should also have two significant figures. So, we round the number to 7.6.
Adding 7.6 to 509.15 gives us 516.75. Here, 509.15 has five significant figures, but the addition and subtraction operations only retain as many decimal places as the number with the fewest decimal places, which, in this case, is 7.6. Therefore, we round the result to the nearest hundredth, which is 516.78.
For the second expression: (154+8446.1)/54
Adding 154 to 8446.1 gives us 8600.1. It has five significant figures since both numbers involved have three significant figures each.
Dividing 8600.1 by 54 yields 159.259259259. The number 54 has two significant figures, and the division operation retains as many decimal places as the number with the fewest decimal places, which is 54. Therefore, we round the result to the nearest thousandth, which is 159.261.
I hope this explanation helps! Let me know if you have any further questions.