From personal advice to professional guidance, IDNLearn.com has the answers you seek. Find the solutions you need quickly and accurately with help from our knowledgeable community.
Sagot :
Sure! Let's solve each of these operations step-by-step, ensuring that the results have the correct number of significant figures.
### a) [tex]\( 4.085 \times 10^{-3} \div 2.367 \)[/tex]
1. Calculate the division:
[tex]\[ 4.085 \times 10^{-3} \div 2.367 \approx 0.00172581326573722 \][/tex]
2. Determine the number of significant figures. The operand with the least significant figures is [tex]\(2.367\)[/tex] (4 significant figures).
3. Round the result to 4 significant figures:
[tex]\[ 0.001726 \][/tex]
Therefore, the result is [tex]\(0.001726\)[/tex] with 4 significant figures.
### b) [tex]\( 68 - 22.4 \)[/tex]
1. Calculate the subtraction:
[tex]\[ 68 - 22.4 = 45.6 \][/tex]
2. Determine the number of significant figures. The operand [tex]\(68\)[/tex] has 2 significant figures while [tex]\(22.4\)[/tex] has 3 significant figures. In subtraction or addition, the result should be rounded to the least number of decimal places, which is 0 decimal places (for [tex]\(68\)[/tex]).
3. Round the result:
[tex]\[ 46 \][/tex]
Therefore, the result is [tex]\(46\)[/tex] with 2 significant figures.
### c) [tex]\( \frac{6.780 \times 5.6}{345.18} \)[/tex]
1. Calculate the multiplication and division:
[tex]\[ \frac{6.780 \times 5.6}{345.18} \approx 0.10999478532939334 \][/tex]
2. Determine the number of significant figures. The operand [tex]\(5.6\)[/tex] has the least significant figures (2 significant figures).
3. Round the result to 2 significant figures:
[tex]\[ 0.11 \][/tex]
Therefore, the result is [tex]\(0.11\)[/tex] with 2 significant figures.
### d) [tex]\( 352.64 + 73.5 + 10 \)[/tex]
1. Calculate the addition:
[tex]\[ 352.64 + 73.5 + 10 = 436.14 \][/tex]
2. Determine the number of significant figures. The operand [tex]\(10\)[/tex] has 2 significant figures but no decimal places; hence, we consider the operand with no decimal places (10).
3. Round the result to 0 decimal places:
[tex]\[ 436 \][/tex]
Therefore, the result is [tex]\(436\)[/tex] with 0 decimal places (as significant figures).
### e) [tex]\( 3.64 \times 10^{-5} \times 4.5 \times 10^9 \)[/tex]
1. Calculate the multiplication:
[tex]\[ 3.64 \times 10^{-5} \times 4.5 \times 10^9 \approx 163800.0 \][/tex]
2. Determine the number of significant figures. The operands [tex]\(3.64 \times 10^{-5}\)[/tex] and [tex]\(4.5 \times 10^9\)[/tex] have the least significant number which is 2 significant figures.
3. Round the result to 2 significant figures:
[tex]\[ 1.6 \times 10^5 \][/tex]
Therefore, the result is [tex]\(1.6 \times 10^5\)[/tex] with 2 significant figures.
### f) [tex]\( \frac{42.47 - 2.690 + \log(3.110 \times 10^2)}{(12.30 - 2.804) \times 4.2001} \)[/tex]
1. Calculate each component:
[tex]\[ 42.47 - 2.690 + \log(3.110 \times 10^2) \approx 42.47 - 2.690 + 2.493 = 42.273 \][/tex]
[tex]\[ (12.30 - 2.804) \times 4.2001 \approx 9.496 \times 4.2001 \approx 39.877896 \][/tex]
2. Perform the final division:
[tex]\[ \frac{42.273}{39.877896} \approx 1.0598887230386589 \][/tex]
3. Determine the number of significant figures. The operand [tex]\(2.804\)[/tex] has the least significant figures (3 significant figures).
4. Round the result to 3 significant figures:
[tex]\[ 1.06 \][/tex]
Therefore, the result is [tex]\(1.06\)[/tex] with 3 significant figures.
In summary, the results with the correct number of significant figures are as follows:
a) [tex]\(0.001726\)[/tex]
b) [tex]\(46\)[/tex]
c) [tex]\(0.11\)[/tex]
d) [tex]\(436\)[/tex]
e) [tex]\(1.6 \times 10^5\)[/tex]
f) [tex]\(1.06\)[/tex]
### a) [tex]\( 4.085 \times 10^{-3} \div 2.367 \)[/tex]
1. Calculate the division:
[tex]\[ 4.085 \times 10^{-3} \div 2.367 \approx 0.00172581326573722 \][/tex]
2. Determine the number of significant figures. The operand with the least significant figures is [tex]\(2.367\)[/tex] (4 significant figures).
3. Round the result to 4 significant figures:
[tex]\[ 0.001726 \][/tex]
Therefore, the result is [tex]\(0.001726\)[/tex] with 4 significant figures.
### b) [tex]\( 68 - 22.4 \)[/tex]
1. Calculate the subtraction:
[tex]\[ 68 - 22.4 = 45.6 \][/tex]
2. Determine the number of significant figures. The operand [tex]\(68\)[/tex] has 2 significant figures while [tex]\(22.4\)[/tex] has 3 significant figures. In subtraction or addition, the result should be rounded to the least number of decimal places, which is 0 decimal places (for [tex]\(68\)[/tex]).
3. Round the result:
[tex]\[ 46 \][/tex]
Therefore, the result is [tex]\(46\)[/tex] with 2 significant figures.
### c) [tex]\( \frac{6.780 \times 5.6}{345.18} \)[/tex]
1. Calculate the multiplication and division:
[tex]\[ \frac{6.780 \times 5.6}{345.18} \approx 0.10999478532939334 \][/tex]
2. Determine the number of significant figures. The operand [tex]\(5.6\)[/tex] has the least significant figures (2 significant figures).
3. Round the result to 2 significant figures:
[tex]\[ 0.11 \][/tex]
Therefore, the result is [tex]\(0.11\)[/tex] with 2 significant figures.
### d) [tex]\( 352.64 + 73.5 + 10 \)[/tex]
1. Calculate the addition:
[tex]\[ 352.64 + 73.5 + 10 = 436.14 \][/tex]
2. Determine the number of significant figures. The operand [tex]\(10\)[/tex] has 2 significant figures but no decimal places; hence, we consider the operand with no decimal places (10).
3. Round the result to 0 decimal places:
[tex]\[ 436 \][/tex]
Therefore, the result is [tex]\(436\)[/tex] with 0 decimal places (as significant figures).
### e) [tex]\( 3.64 \times 10^{-5} \times 4.5 \times 10^9 \)[/tex]
1. Calculate the multiplication:
[tex]\[ 3.64 \times 10^{-5} \times 4.5 \times 10^9 \approx 163800.0 \][/tex]
2. Determine the number of significant figures. The operands [tex]\(3.64 \times 10^{-5}\)[/tex] and [tex]\(4.5 \times 10^9\)[/tex] have the least significant number which is 2 significant figures.
3. Round the result to 2 significant figures:
[tex]\[ 1.6 \times 10^5 \][/tex]
Therefore, the result is [tex]\(1.6 \times 10^5\)[/tex] with 2 significant figures.
### f) [tex]\( \frac{42.47 - 2.690 + \log(3.110 \times 10^2)}{(12.30 - 2.804) \times 4.2001} \)[/tex]
1. Calculate each component:
[tex]\[ 42.47 - 2.690 + \log(3.110 \times 10^2) \approx 42.47 - 2.690 + 2.493 = 42.273 \][/tex]
[tex]\[ (12.30 - 2.804) \times 4.2001 \approx 9.496 \times 4.2001 \approx 39.877896 \][/tex]
2. Perform the final division:
[tex]\[ \frac{42.273}{39.877896} \approx 1.0598887230386589 \][/tex]
3. Determine the number of significant figures. The operand [tex]\(2.804\)[/tex] has the least significant figures (3 significant figures).
4. Round the result to 3 significant figures:
[tex]\[ 1.06 \][/tex]
Therefore, the result is [tex]\(1.06\)[/tex] with 3 significant figures.
In summary, the results with the correct number of significant figures are as follows:
a) [tex]\(0.001726\)[/tex]
b) [tex]\(46\)[/tex]
c) [tex]\(0.11\)[/tex]
d) [tex]\(436\)[/tex]
e) [tex]\(1.6 \times 10^5\)[/tex]
f) [tex]\(1.06\)[/tex]
We greatly appreciate every question and answer you provide. Keep engaging and finding the best solutions. This community is the perfect place to learn and grow together. IDNLearn.com provides the answers you need. Thank you for visiting, and see you next time for more valuable insights.
