Express the product of 3.2 × 10⁶ and 4.1 × 10⁻¹ in the standard form.
Solution:
Given, the product of 3.2 × 10⁶ and 4.1 × 10⁻¹
We have to express the product in the 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.
Product of 3.2 × 10⁶ and 4.1 × 10⁻¹ = 3.2 × 10⁶ × 4.1 × 10⁻¹
= 3.2 × 4.1 × 10⁶ × 10⁻¹
= 13.12 × 10⁶ × 10⁻¹
Using law of exponents,
am × an = am + n
Here, a = 10
m = 6
n = -1
So, m + n = 6 + (-1)
= 6 - 1
= 5
So, 10⁶ × 10⁻¹ = 10⁵
13.12 × 10⁶ × 10⁻¹ = 13.12 × 10⁵
= 1.312 × 10¹ × 10⁵
Using law of exponents,
am × an = am + n
Here, a = 10
m = 1
n = 5
So, m + n = 1 + 5
= 6
So, 10¹ × 10⁵ = 10⁶
1.312 × 10¹ × 10⁵ = 1.312 × 10⁶
Therefore, the required standard form is 1.312 × 10⁶.
✦ Try This: Express the product of 4.5 × 10⁶ and 2.5 × 10⁻¹ in the standard form
☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 12
NCERT Exemplar Class 8 Maths Chapter 8 Problem 108
Express the product of 3.2 × 10⁶ and 4.1 × 10⁻¹ in the standard form.
Summary:
Expressing the product of 3.2 × 10⁶ and 4.1 × 10⁻¹ in the standard form, we get 1.312 × 10⁶.
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