# How do you convert 0.119 into scientific form?

Jul 17, 2015

To bring $0.119$ into the range $\left[1 , 10\right)$, you need to multiply it by $10$ once.

So in scientific form: $0.119 = 1.19 \times {10}^{- 1}$

#### Explanation:

Scientific form expresses a number as a mantissa in the range $\left[1 , 10\right)$ multiplied by an integer power of $10$.

In our example, $0.119 < 1$, so will have a negative exponent (power of $10$).

To bring $0.119$ into the range $\left[1 , 10\right)$, we need to multiply it by ${10}^{1}$, shifting it one place to the left to get $1.19$. To compensate for the fact that we have multiplied it by ${10}^{1}$ we use an exponent of $- 1$ to get:

$0.119 = 1.19 \times {10}^{- 1}$