Solved Examples, Assignments, and Numerical Problems of Chapter 1| Physical quantities and Measurements | Physics Class 9 Notes

Solution to Examples

1. Solved Examples on "Standard form / Scientific Notation"

Example 1.1: Average distance between earth and moon

The average distance between the earth and the moon is 384,400,000 m. Write this number in standard form/ scientific notation.

Solution: For scientific notation we have

    N = M x 10ⁿ
    Here N (distance) = 384,000,000 m, M = 3.84400000 (because to get mantissa we have to move the decimal point and place it after 1st non-zero digit.), and 10ⁿ= 10⁸ (because the decimal is moved by 8 digits towards left), thus

Distance = 3.84400000 x 10⁸ m or 3.844 x 10⁸ m.     Answer

Solution to Assignments

1. Solved Numericals on "Standard form / Scientific Notation"

Assignment 1.1: Mass of earth

The mass of Earth is 5,980,000,000,000,000,000,000,000 kg, write this number in Standard form/ Scientific notation.

Solution: For scientific notation we have

    N =M x 〖10ⁿ〗
    Here N (mass) = 5,980,000,000,000,000,000,000,000 kg, M = 5.980,000,000,000,000,000,000,000 kg (because to get mantissa we have to move the decimal point and place it after 1st non-zero digit.) and     10ⁿ= 10¹⁰ (because decimal is moved by 10 digits towards left), thus

    Mass = 5.98 x 〖10²⁴〗kg.    Answer 

Assignment 1.2: Seconds in a week

Calculate the number of seconds in a week. Express the number in a power of 10 notation.

Solution

1. Number of seconds in a week

In this case, the conversion factors are                                                                      

day = 24 hours, hour = 60 minutes and minute = 60 seconds, thus                  

7d = 7d x (24 h) / 1d x 60m/1h x 60s/1m
7d = 7 x 24 x 60 x 60 s
7d=604,800 s               Answer

2. Number of seconds in a week written in scientific notation/ standard notation

For scientific notation, we have           N=M x 〖10ⁿ〗

Here N (seconds) = 604,800 s, M = 6.04800

(because to get mantissa we have to move the decimal point and place it after 1^st non-zero   digit.) and 10ⁿ= 10⁵ (because decimal is moved by 5 digits towards left), thus

604,800 Seconds = 6.048 x 〖10⁵〗s                 Answer.

Example 1.3: Smallest molecule

The smallest molecule is the diatomic Hydrogen (H₂), with a bond length of 0.000,000,000,074 m. Write the number in standard form. 

Solution

For scientific notation/standard form, we have

N=M x 〖10〗^n

Here N (bond length) = 0.000,000,000,074 m,  M=7.4 

(because to get   mantissa we have to move the decimal point and place it after 1^st non-zero digit.) and 

10ⁿ= 10^-11 (because decimal is moved by 11 digits towards right), thus

bond length = 7.4 x 10^-11  m