Ex.12.2 Q2 Exponents and Powers - NCERT Maths Class 8

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Question

 Express the following numbers in usual form.

(i) \(3.02 \times 10^{-6}\)

(ii) \(4.5 \times 10^{4}\)

(iii) \(\begin{align}\text{3 }\!\!\times\!\!\text{ 1}{{\text{0}}^{-8}}\end{align}\)

(iv) \(1.0001 \times 10^{9}\)

(v) \(5.8 \times 10^{12}\)

(vi) \(3.61492 \times 10^{6}\)

Text Solution

 

What is known?

Standard form

What is unknown?

Usual form

Reasoning:

As we know standard form of any small or larger number is \(a.b \times {10^n}\),Where \(a\) is a whole number, \(b\) is a decimal number and \(n\) is an integer

For small number \(n\) is negative and for large number \(n\) is positive. So, to convert a small number to its usual form we need to move decimal to its left by number of steps given as exponent values.

Steps:

(i) \(\,3.02 \times {10^{ - 6}}\)

\(\therefore\) Its usual form is

\[\begin{align}3.02 \times {10^{ - 6}} &= \frac{{3.02}}{{1000000}}\\&= 0.00000302\end{align}\]

(ii) \(\,4.5 \times {10^4}\)

Now to convert a big number to its usual form we need to move decimal to its right by number of steps given as its exponent.

\[4.5 \times {10^4}= 45000\]

\(\therefore\) Answer is \(45000\)

(iii) \(\,3 \times {10^{ - 8}} = {{ }}0.00000003\)

(iv) \(1.0001 \times {10^9} = 1000100000\)

(v) \(\,5.8 \times {10^{12}} = {{ }}5800000000000\)

(vi) \(\,3.61492 \times {10^6} = 3614920\)

  
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