Answer

Verified

407.7k+ 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.

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

Mark and label the given geoinformation on the outline class 11 social science CBSE

When people say No pun intended what does that mea class 8 english CBSE

Name the states which share their boundary with Indias class 9 social science CBSE

Give an account of the Northern Plains of India class 9 social science CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Trending doubts

Difference Between Plant Cell and Animal Cell

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Which are the Top 10 Largest Countries of the World?

Give 10 examples for herbs , shrubs , climbers , creepers

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

How do you graph the function fx 4x class 9 maths CBSE

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

Change the following sentences into negative and interrogative class 10 english CBSE