# Question 0a990

Jul 1, 2015

The answer is B) $1.72 \cdot {10}^{- 10} \text{m}$.

#### Explanation:

Scientific notation uses this format to express numbers

$x \cdot {10}^{y}$, where

$x$ - any real number that satisfies the condition $1 \le | x | < 10$, also called the mantissa;
$y$ - any integer number;

So, in your case, you need to select a mantissa that's bigger than or equal to 1, but smaller than 10.

If you look at the, you can "push" the decimal one unit to the right to see what the exponent, or $y$, will be. Moving the decimal to the right implies that the exponent is negative.

$0.000000000172$
$00.00000000172$ $\to$ $y = - 1$
$000.0000000172$ $\to$ $y = - 2$
$0000.000000172$ $\to$ $y = - 3$
$\vdots$
$00000000001.72$ $\to$ $y = - 10$

And there you have it. The mantissa will be $1.72$ and the exponent will be $- 10$. Therefore, the scientific notation for your number is

color(green)(1.72 * 10^(-10)"m"#