Express 1.5 × 10⁶/2.5 × 10⁻⁴ in the standard form.
Solution:
Given, 1.5 × 10⁶/2.5 × 10⁻⁴
We have to express the given term 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.
1.5 × 10⁶/2.5 × 10⁻⁴ = (1.5/2.5) × (10⁶/10⁻⁴)
= 0.6 × (10⁶/10⁻⁴)
Using law of exponents,
am ÷ an = am - n
Here, a = 10
m = 6
n = -4
So, m - n = 6 - (-4)
= 6 + 4
= 10
So, 10⁶ × 10⁻⁴ = 1010
0.6 × (10⁶/10⁻⁴) = 0.6 × 1010
= 6 × 10⁻¹ × 1010
Using law of exponents,
am × an = am + n
Here, a = 10
m = -1
n = 10
So, m + n = -1 + 10
= 9
So, 10⁻¹ × 1010 = 10⁹
6 × 10⁻¹ × 1010 = 6 × 10⁹
Therefore, the required standard form is 6 × 10⁹.
✦ Try This: Express 100 × 10⁶/25 × 10⁻⁴ in the standard form.
☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 12
NCERT Exemplar Class 8 Maths Chapter 8 Problem 109
Express 1.5 × 10⁶/2.5 × 10⁻⁴ in the standard form.
Summary:
Expressing 1.5 × 10⁶/2.5 × 10⁻⁴ in the standard form, we get 6 × 10⁹ using the laws of exponents
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