An aeroplane flies at a speed of 7 . 0 × 10 4 metres per hour. How long will it take to cover a distance of 3 . 5 × 10 5 km ?

Speed of aeroplane = 7.0 × 10 4 m / h o u r Aeroplane fly over a distance = 3 .5 × 10 5 km We know that time = distance speed So, the time will take to cover distance = d i s t a n c e s p e e d = 3.5 × 10 5 k m 7.0 × 10 4 m / h o u r = 3.5 × 10 5 × 10 3 m 7.0 × 10 4 m / h o u r = 35 70 × 10 10 × 10 5 10 4 × 10 3 hours = 5 × 10 3 hrs Therefore, the time taken to cover the distance of 3 . 5 × 10 5 km is 5 × 10 3 hrs .

A city has a population of 1 . 678 × 10 12 . How much is this when expanded?

The population of the city is 1 . 678 × 10 12 . To convert a big number (positive powers of 10 ) from its standard form to its usual form shift the decimal point towards the right by the number of places equivalent to the power of 10 . In doing so, fill up the places on the right by zeros as many as necessary. Thus, we have, 1 . 678 × 10 12 = 1678000000000 [Shift the decimal point 12 places to the right] Therefore, the required answer is 1678000000000 .

The star sirius is about 8 . 1 × 10 13 km from the earth. Assuming that light travels at a speed of 3 . 0 × 10 5 km per second, find how long will the light from sirius take to reach the earth?

The distance of star sirius from the earth is 8 . 1 × 10 13 km. The light travels at a speed of 3 . 0 × 10 5 km/sec. If a quantity is written as the product of a power of 10 and a number that is greater than or equal to 1 and less than 10 , then the quantity is said to be in scientific notation. So, the time will take to cover distance = d i s t a n c e s p e e d = 8 . 1 × 10 13 k m 3 .0 × 10 5 km / sec = 8 . 1 × 10 13 km 3 .0 × 10 5 km / sec = 8 . 1 3 . 0 × 10 13 10 5 sec = 2 . 7 × 10 8 sec Therefore, the time taken to cover the distance of 8 . 1 × 10 13 km is 2 . 7 × 10 8 sec .

E M B I B E

Maths Hub (ICSE)>Chapter 2 - Exponents and Powers>CHECK POINT

S Purkayastha Solutions for Chapter: Exponents and Powers, Exercise 3: CHECK POINT

Author:S Purkayastha

S Purkayastha Mathematics Solutions for Exercise - S Purkayastha Solutions for Chapter: Exponents and Powers, Exercise 3: CHECK POINT

Attempt the free practice questions on Chapter 2: Exponents and Powers, Exercise 3: CHECK POINT with hints and solutions to strengthen your understanding. Maths Hub (ICSE) solutions are prepared by Experienced Embibe Experts.

Questions from S Purkayastha Solutions for Chapter: Exponents and Powers, Exercise 3: CHECK POINT with Hints & Solutions

EASY

8th ICSE

IMPORTANT

Maths Hub (ICSE)>Chapter 2 - Exponents and Powers>CHECK POINT>Q 1

Express $44$ in scientific notation.

MEDIUM

8th ICSE

IMPORTANT

Maths Hub (ICSE)>Chapter 2 - Exponents and Powers>CHECK POINT>Q 4

An aeroplane flies at a speed of $7.0 \times 10^{4}$ metres per hour. How long will it take to cover a distance of $3.5 \times 10^{5} km ?$

EASY

8th ICSE

IMPORTANT

Maths Hub (ICSE)>Chapter 2 - Exponents and Powers>CHECK POINT>Q 5

A city has a population of $1.678 \times 10^{12}$ . How much is this when expanded?

EASY

8th ICSE

IMPORTANT

Maths Hub (ICSE)>Chapter 2 - Exponents and Powers>CHECK POINT>Q 6

The mean distance of the moon from the earth is $384400000$ metres. Express the distance in scientific notation.

EASY

8th ICSE

IMPORTANT

Maths Hub (ICSE)>Chapter 2 - Exponents and Powers>CHECK POINT>Q 7

The distance of the earth from the sun is $149000000$ km. How long will a sunray take to reach the earth if it travels at a speed of $3.0 \times 10^{5} km / s$ ?

EASY

8th ICSE

IMPORTANT

Maths Hub (ICSE)>Chapter 2 - Exponents and Powers>CHECK POINT>Q 8

Express one second in a year in scientific notation.

EASY

8th ICSE

IMPORTANT

Maths Hub (ICSE)>Chapter 2 - Exponents and Powers>CHECK POINT>Q 9

The number of red cells per cubic mm of human body is approximately $5.5$ million. Express it in scientific notation.

EASY

8th ICSE

IMPORTANT

Maths Hub (ICSE)>Chapter 2 - Exponents and Powers>CHECK POINT>Q 10

The star sirius is about $8.1 \times 10^{13}$ km from the earth. Assuming that light travels at a speed of $3.0 \times 10^{5}$ km per second, find how long will the light from sirius take to reach the earth?

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