Answer
384.6k+ views
Hint:
Here, we will substitute the values of the given variable in the given equation. We will then simplify it using the exponent rule. We will then use the basic mathematical operation to get the simplified value of \[R\]. Then we will write the answer to an appropriate degree of accuracy by observing the position of the decimal point in the question. The appropriate degree of accuracy is a measure of how close and correct a stated value is to the actual, real value being described.
Complete step by step solution:
It is given that \[R = \dfrac{{{x^2}}}{y}\], where, \[x = 3.8 \times {10^5}\] and \[y = 5.9 \times {10^4}\]
Substituting these values in \[R\], we get,
\[R = \dfrac{{{{\left( {3.8 \times {{10}^5}} \right)}^2}}}{{5.9 \times {{10}^4}}}\]
Using the identity \[{\left( {a \times b} \right)^m} = {a^m} \times {b^m}\] and \[{\left( {{a^m}} \right)^n} = {a^{m \times n}}\], we get,
\[ \Rightarrow R = \dfrac{{{{\left( {3.8} \right)}^2} \times {{10}^{5 \times 2}}}}{{5.9 \times {{10}^4}}} = \dfrac{{14.44 \times {{10}^{10}}}}{{5.9 \times {{10}^4}}}\]
Now, using the identity \[\dfrac{{{a^m}}}{{{a^n}}} = {a^{m - n}}\] and dividing \[14.44\] by \[5.9\], we get,
\[ \Rightarrow R = 2.447 \times {10^{10 - 4}} = 2.447 \times {10^6}\]
Now, we can see that the decimal values given in the question in \[x\] and \[y\] are to 1 decimal place, thus, we will give our answer to an appropriate degree of accuracy to 1 decimal place only.
Thus, we get,
\[R = 2.447 \times {10^6} \approx 2.4 \times {10^6}\]
Hence, the value of \[R\] giving an answer in standard form to an appropriate degree of accuracy is \[2.4 \times {10^6}\].
Thus, this is the required answer.
Note:
Accuracy may be affected by rounding, the use of significant figures or ranges in measurement. In maths “to an appropriate degree of accuracy” means that the question wants us to present our answer in the same form as the least accurate measure in the question. Also, we should know that the accuracy of a measurement or approximation is the degree of closeness to the exact value whereas the error is the difference between the approximation and the exact value. Hence, approximation and error are complete different terms.
Here, we will substitute the values of the given variable in the given equation. We will then simplify it using the exponent rule. We will then use the basic mathematical operation to get the simplified value of \[R\]. Then we will write the answer to an appropriate degree of accuracy by observing the position of the decimal point in the question. The appropriate degree of accuracy is a measure of how close and correct a stated value is to the actual, real value being described.
Complete step by step solution:
It is given that \[R = \dfrac{{{x^2}}}{y}\], where, \[x = 3.8 \times {10^5}\] and \[y = 5.9 \times {10^4}\]
Substituting these values in \[R\], we get,
\[R = \dfrac{{{{\left( {3.8 \times {{10}^5}} \right)}^2}}}{{5.9 \times {{10}^4}}}\]
Using the identity \[{\left( {a \times b} \right)^m} = {a^m} \times {b^m}\] and \[{\left( {{a^m}} \right)^n} = {a^{m \times n}}\], we get,
\[ \Rightarrow R = \dfrac{{{{\left( {3.8} \right)}^2} \times {{10}^{5 \times 2}}}}{{5.9 \times {{10}^4}}} = \dfrac{{14.44 \times {{10}^{10}}}}{{5.9 \times {{10}^4}}}\]
Now, using the identity \[\dfrac{{{a^m}}}{{{a^n}}} = {a^{m - n}}\] and dividing \[14.44\] by \[5.9\], we get,
\[ \Rightarrow R = 2.447 \times {10^{10 - 4}} = 2.447 \times {10^6}\]
Now, we can see that the decimal values given in the question in \[x\] and \[y\] are to 1 decimal place, thus, we will give our answer to an appropriate degree of accuracy to 1 decimal place only.
Thus, we get,
\[R = 2.447 \times {10^6} \approx 2.4 \times {10^6}\]
Hence, the value of \[R\] giving an answer in standard form to an appropriate degree of accuracy is \[2.4 \times {10^6}\].
Thus, this is the required answer.
Note:
Accuracy may be affected by rounding, the use of significant figures or ranges in measurement. In maths “to an appropriate degree of accuracy” means that the question wants us to present our answer in the same form as the least accurate measure in the question. Also, we should know that the accuracy of a measurement or approximation is the degree of closeness to the exact value whereas the error is the difference between the approximation and the exact value. Hence, approximation and error are complete different terms.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Why Are Noble Gases NonReactive class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let X and Y be the sets of all positive divisors of class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
At which age domestication of animals started A Neolithic class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Write a letter to the principal requesting him to grant class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)