Question 11 :
The diameter of the Sun is $1.4 × 10^9$ m and the diameter of the Earth is $1.2756 × 10^7$ m. What is the comparison between their diameters by division?

Question 12 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1ccd0f59b460d7261edf0.PNG' /> Refer to the above image. Determine whether there is a single repeater machine that will do the same work. If so, describe it.

Question 15 :
The distance between earth and sun is 150 million kilometres which can be written in exponential form as _______.

Question 16 :
Find the value of m for which, $5^m÷ 5^{– 3} = 5^5$

Question 17 :
If a = – 1, b = 2, then find the value of $a^b-b^{a}$

Question 19 :
State true or false: Standard form is also called scientific notation form.

Question 22 :
Express in standard form: Charge of an electron is 0.000,000,000,000,000,000,16 coulomb.

Question 23 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1ccd7f59b460d7261edfa.PNG' /> The above table may help. Long back in ancient times, a farmer saved the life of a king’s daughter. The king decided to reward the farmer with whatever he wished. The farmer, who was a chess champion, made an unusal request: “I would like you to place 1 rupee on the first square of my chessboard, 2 rupees on the second square, 4 on the third square, 8 on the fourth square, and so on, until you have covered all 64 squares. Each square should have twice as many rupees as the previous square.” The king thought this to be too less and asked the farmer to think of some better reward, but the farmer didn’t agree. How much money has the farmer earned?

Question 25 :
A particular star is at a distance of about $8.1\times10^{13}$ km from the Earth. Assuring that light travels at $3\times10^8$ m per second, find how long does light takes from that star to reach the Earth.

Question 28 :
Express in standard form: Size of a plant cell is 0.00001275 m

Question 30 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1ccd0f59b460d7261edf1.PNG' /> Refer to the above image. Shikha has an order from a golf course designer to put palm trees through a $(× 2^3)$ machine and then through a $(× 3^3)$ machine. She thinks she can do the job with a single repeater machine. What single repeater machine should she use?

Question 31 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1ccd4f59b460d7261edf6.PNG' /> From the above figure, supply the missing information for diagram.

Question 34 :
Express the result in power notation with positive exponent.$(-4)^5 ÷ (-4)^8$

Question 40 :
Simplify and write the answer in the exponential form. $(2^5÷ 2^8)^5 \times 2^{– 5}$

Question 41 :
In a stack there are 5 books each of thickness 20 mm and 5 paper sheets each of thickness 0.016 mm. What is the total thickness of the stack?

Question 48 :
Find the value of $(2^{– 1} × 4^{– 1}) ÷ 2^{– 2}$