0.0016 in index form

asked by guest
on Nov 25, 2024 at 4:50 am



You asked:

Convert \(0.0016\) into index form.

MathBot Answer:

The index form of \(0.0016\) is \(\dfrac{1}{5^4}\)

 The index form of a number is that number written as an exponential expression. You can put a fraction in index form by taking the prime factorization of both the numerator and denominator.


 The prime factorization of an integer is the decomposition of that integer into the product of powers of prime numbers. Begin by listing the first ten primes: $2,3,5,7,11,13,17,19,23,29$.


 Divide the integer by the smallest divisible prime. Then divide the result by its smallest divisible prime. Continue until the result is prime, and multiply the primes together to get the prime factorization.


\(1\) is prime.

$$\begin{aligned}5&\underline{\big | 625}\\5&\underline{\big | 125}\\5&\underline{\big | 25}\\& \: \: 5\end{aligned}$$

$625 = 5 \cdot 5 \cdot 5 \cdot 5 = 5^4$

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