Express each of the following in standard form: A Helium atom has a diameter of 0.000000022 cm.

Solution:

Given, a Helium atom has a diameter of 0.000000022 cm.

We have to write in standard form.

Any number can be expressed as decimal numbers between 1 and 10 multiplied by a power of 10. This form of representation is termed as the standard form.

0.000000022 = 22/10⁹

Using law of exponents,

a⁻ⁿ = 1/aⁿ

1/10⁹ = 10⁻⁹

So, 22/10⁹ = 22 × 10⁻⁹

= 2.2 × 10¹ × 10⁻⁹

Using law of exponents,

a^m × aⁿ = a^{m + n}

Here, a = 10

m = 1

n = -9

So, m + n = 1 + (-9)

= 1 - 9

= -8

10¹ × 10⁻⁹ = 10⁻⁸

So, 2.2 × 10¹ × 10⁻⁹ = 2.2 × 10⁻⁸

Therefore, the diameter of Helium atom is 2.2 × 10⁻⁸ cm.

✦ Try This: Express in standard form: A Hydrogen atom has a diameter of 0.000000042 cm.

☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 12

NCERT Exemplar Class 8 Maths Chapter 8 Problem 115(b)

Express each of the following in standard form: A Helium atom has a diameter of 0.000000022 cm.

Summary:

The diameter of Helium atom in standard form is 2.2 × 10⁻⁸ cm using the law of exponents

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