ICSE Class 8 Answered

What is the order of magnitude of following physical quantities? (i) 1,400,000,000,000,000 m (ii) 1,390,000,000 m (iii) 0.000000000106 gm (iv) 1 / 700000 [10 raised to 15,10 raised to 9 ,10 raised to –10,10 raised to –5]

Asked by shreyashsingh1000 | 05 May, 2020, 09:43: PM

Expert Answer

Let's understand first how to find the order of magnitude: -

In scientific notations, the numbers are expressed as,

Number = A × 10^x

Here, A - Can be any number lying between 1 and 10

x - integer (power of 10)

Order of magnitude of any given quantity is in the form of 10^x

For determining the power, the value (number) of the quantity in the place of A is rounded off.

If A<5 then ignore it and keep power of 10 as it is.

If A>5 or A = 5 then add '1' to power of 10.

For e.g. -

1. Speed of light is 3×10⁸ m/s

Thus, order of magnitude is ≈ 10⁸ m/s ( as 3<5)

2. Mass of electron is 9.1×10^-31 kg

Thus, oder of magnitude is ≈ 10^-31+1 ≈ 10^-30 kg (as 9.1>5)

Now, let's see what is the order of magnitude in given question: -

i) 1,400,000,000,000,000 m = 1.4 × 10¹⁵ m

Thus, order of magnitude is ≈ 10¹⁵ m (Since, 1.4 < 5)

ii) 1,390,000,000 m = 1.39 × 10⁹ m

Thus, order of magnitude is ≈ 10⁹ m ( As 1.39 is less than 5)

iii) 0.000000000106 g = 1.06×10^-10 g

Thus, order of magnitude ≈ 10^-10 g

i v right parenthesis space 1 over 700000 equals fraction numerator 1 over denominator 7 cross times 10 to the power of 5 end fraction space equals space 1 over 7 cross times 10 to the power of negative 5 end exponent space equals space 0.142 cross times 10 to the power of negative 5 end exponent space equals space 1.4 space cross times space 10 to the power of negative 1 end exponent cross times 10 to the power of negative 5 end exponent space equals space 1.4 cross times 10 to the power of negative 6 end exponent T h u s comma space o r d e r space o f space m a g n i t u d e space almost equal to 10 to the power of negative 6 end exponent

Answered by Shiwani Sawant | 05 May, 2020, 11:44: PM

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