Write 0.000005678 in the standard form.
Solution:
Given, the number is 0.000005678.
We have to find 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.
0.000005678 = 0.5678/100000
= 0.5678/10⁵
Using law of exponents,
a⁻ⁿ = 1/aⁿ
= 0.5678 × 10⁻⁵
= 5.678 × 10¹ × 10⁻⁵
Using law of exponents,
am × an = am + n
Here, a = 10
m = 1
n = -5
So, m + n = 1 + (-5)
= 1 - 5
= -4
So, 10¹ × 10⁻⁵ = 10⁻⁴
5.678 × 10¹ × 10⁻⁵ = 5.678 × 10⁻⁴
Therefore, the required standard form is 5.678 × 10⁻⁴.
✦ Try This: Write 0.000004321 in the standard form.
☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 12
NCERT Exemplar Class 8 Maths Chapter 8 Problem 107
Write 0.000005678 in the standard form.
Summary:
The standard form of 0.000005678 is 5.678 × 10⁻⁴ using the law of exponents a⁻ⁿ = 1/aⁿ
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