Calculate the following and round to the allowed number of significant figures
1. (18.00 x 1.5) / 0.00625
2.4.61 X 10^3 / 5.1008 x 10^-4
My answers
1. 4320
2. 9.037 x 10^-1
Please explain what I did wrong if I'm incorrect.
Thank you
For #1 your digits are right but not the s.f. You are allowed only 2 places (because of the 1.5) so your answer should be 4.3E3
For #2, I think you keyed in 4.61E-3 instead of 4.61E3.
The answer is 9.0377E6 and you are allowed 3 places so that should be rounded to 9.04E6.
Well, it looks like you're missing a few significant figures in your answers. Let me help you out with the calculations:
1. (18.00 x 1.5) / 0.00625
= 27 / 0.00625
= 4320
So you got that one right! Good job!
2. (4.61 x 10^3) / (5.1008 x 10^-4)
= 4.61 / 0.00051008
= 9026.226
Now, we need to round to the correct number of significant figures. The number with the least number of significant figures is 4.61, which has three digits. So the final answer should have three significant figures as well:
2. 9.03 x 10^3
So, you were really close on this one! Just remember to pay attention to the significant figures when rounding your answers. Keep up the good work!
Let's go through the calculations step by step:
1. (18.00 x 1.5) / 0.00625
First, multiply 18.00 by 1.5:
18.00 x 1.5 = 27.00
Then, divide the result by 0.00625:
27.00 / 0.00625 = 4320
Therefore, your answer for the first calculation, 4320, is correct.
2. 4.61 x 10^3 / 5.1008 x 10^-4
To divide the numbers in scientific notation, we need to divide their coefficients and subtract their exponents:
4.61 / 5.1008 = 0.9037
Now, subtract the exponents:
10^3 / 10^-4 = 10^(3-(-4)) = 10^7
Combining the coefficient and exponent:
0.9037 x 10^7
Therefore, your answer for the second calculation should be 0.9037 x 10^7, or in scientific notation, 9.037 x 10^6, not 9.037 x 10^-1 as you stated.
To round this answer to the allowed number of significant figures, we need to check the significant figures in the original numbers. Since both numbers given have three significant figures, the answer should also have three significant figures. Therefore, the rounded answer is 9.04 x 10^6.
So, the correct answer for the second calculation is 9.04 x 10^6, instead of 9.037 x 10^-1.
To calculate the given expressions and round to the allowed number of significant figures, we need to consider the rules for significant figures.
1. (18.00 x 1.5) / 0.00625
To determine the significant figures, we look at the original values:
18.00 has four significant figures.
1.5 has two significant figures.
0.00625 has four significant figures.
The multiplication of 18.00 and 1.5 gives 27.00, but since the given values have limited significant figures, we round it to two significant figures, which is 27.
Now, we divide 27 by 0.00625. To preserve significant figures, we use the same number of significant figures as the original values, which is four. So, the division becomes 27.00 / 0.00625 = 4320.
From your answer, it seems you rounded the final result to a whole number, which is incorrect. The correct answer, rounded to the allowed significant figures, is 4320.
2. 4.61 x 10^3 / 5.1008 x 10^-4
To simplify this expression, we can rewrite both numbers with the same exponent:
4.61 x 10^3 becomes 4610 x 10^-1 (moving decimal once to the left)
5.1008 x 10^-4 remains the same
Now, we divide 4610 by 5.1008. To determine the number of significant figures, we look at the original values:
4610 has three significant figures.
5.1008 has five significant figures.
To preserve significant figures in the division, we use the same number as the original values, which is three. So, the division becomes 4610 / 5.1008 = 902.7927...
To round this result to the allowed significant figures, we keep three significant figures, which gives us 902.
However, the multiplication of 10^-1 (0.1) and 10^-4 (0.0001) shifts the decimal four places to the left. Therefore, the answer becomes 9.02 x 10^-1 (0.902 in standard form).
From your answer, it seems you rounded the final result to three decimal places, which is incorrect. The correct answer, rounded to the allowed significant figures, is 9.02 x 10^-1.