Samacheer Kalvi 8th Maths Guide Chapter 1 Numbers Ex 1.7

Samacheer Kalvi 8th Maths Guide Chapter 1 Numbers Ex 1.7

Tamilnadu Samacheer Kalvi 8th Maths Solutions Chapter 1 Numbers Ex 1.7

Miscellaneous Practice Problems

Question 1.

Powers of 2:
2, 4, 8, 16, 32, 64, 128, 256, 512,….

Question 10.
Give the answer in scientific notation:
A human heart beats at an average of 80 beats per minute. How many times does it beat in
i) an hour?
ii) a day?
iii) a year?
iv) 100 years?
Answer:
Heart beat per minute = 80 beats
(i) an hour
One hour = 60 minutes
Heart beat in an hour = 60 × 80
= 4800
= 4.8 × 10³

(ii) In a day
One day = 24 hours = 24 × 60 minutes
∴ Heart beat in one day = 24 × 60 × 80 = 24 × 4800 = 115200
= 1.152 × 10⁵

(iii) a year
One year = 365 days = 365 × 24 hours = 365 × 24 × 60 minutes
∴ Heart beats in a year = 365 × 24 × 60 × 80
= 42048000
= 4.2048 × 10⁷

(iv) 100 years
Heart beats in one year = 4.2048 × 10⁷
heart beats in 100 years = 4.2048 × 10⁷ × 100 = 4.2048 × 10⁷ × 10²
= 4.2048 × 10⁹

Challenging Problems:

Question 14.

Question 16.

Answer:

Answer:

Question 17.
A group of 1536 cadets wanted to have a parade forming a square design. Is it possible? If it is not possible, how many more cadets would be required?
Answer:
Number of cadets to form square design


The numbers 2 and 3 are unpaired
∴ It is impossible to have the parade forming square design with 1536 cadets.

39 × 39 = 1521
Also 40 × 40 = 1600
∴ We have to add (1600 – 1536) = 64 to make 1536 a perfect square.
∴ 64 more cadets would be required to form the square design.

Question 20.
Order the following from the least to the greatest: 16²⁵, 8¹⁰⁰, 3⁵⁰⁰, 4⁴⁰⁰, 2⁶⁰⁰
Answer:
16²⁵ = (2⁴)²⁵ = 2¹⁰⁰
8¹⁰⁰ = (2³)¹⁰⁰ = 2³⁰⁰
4⁴⁰⁰ = (2²)⁴⁰⁰ = 2⁸⁰⁰
2⁶⁰⁰ = 2⁶⁰⁰
Comparing the powers we have.
2¹⁰⁰ < 2³⁰⁰ < 2⁶⁰⁰ < 2⁸⁰⁰
∴ The required order: 16²⁵, 8¹⁰⁰, 3⁵⁰⁰, 4⁴⁰⁰, 2⁶⁰⁰