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 unusual 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 tothink of some better reward, but the farmer didn’t agree.

How much money has the farmer earned?

[Hint: The following table may help you. What is the first square on which the king will place at least Rs 10 lakh?]

State whether the given statements are true (T)or false (F).

329.25 = 3 × 10² + 2 × 101 + 9 × 10⁰ + 2 × 10^–1 + 5 × 10^–2

The paper clip below has the indicated length. What is the length in standard form.

There are 864,00 seconds in a day. How many days long is a second?

Express your answer in scientific notation.

Find the value of n.

Solve:

At the end of the 20th century, the world population was approximately 6.1 × 10⁹ people. Express this population in usual form. How would you say this number in words?

The number of red blood cells per cubic millimetre of blood is approximately 5.5 million. If the average body contains 5 litres of blood, what is the total number of red cells in the body? Write the standard form. (1 litre = 1,00,000 mm3)

Astronomy The table shows the mass of the planets, the sun and the moon in our solar system.

A. Write the mass of each planet and the Moon in scientific notation.

B. Order the planets and the moon by mass, from least to greatest.

C. Which planet has about the same mass as earth?

The left column of the chart lists the lengths of input pieces of ribbon. Stretching machines are listed across the top. The other entries are the the outputs for sending the input ribbon from that row through the machine from that column. Copy and complete the chart.

The left column of the chart lists the lengths of input chains of gold. Repeater machines are listed across the top. The other entries are the outputs you get when you send the input chain from that row through the repeater machine from that column. Copy and complete the chart.