# How do you express 0.00000054 in scientific notation?

Apr 3, 2017

We need to write $a \times {10}^{b}$, where $a$ has just one non-zero digit before the decimal point.

#### Explanation:

To change the given number to $5.4$, we need to move the d.p. 7 places to the right. This means that the 10-power is negative and equal to -7.

$= 5.4 \times {10}^{- 7}$

Apr 3, 2017

$5.4 \times {10}^{- 7}$

#### Explanation:

Scientific notation is composed of a "mantissa" and an "exponent".

The mantissa is a decimal number with one non-zero digit to the left of the decimal point (except, of course, if the number is exactly zero).

The "exponent" is $10$ to some power, where the power indicates how many decimal positions the decimal point in the mantissa needs to be moved (to the right if the exponent is positive; to the left if the exponent is negative) to form the actual value of the number.

The mantissa for $0.00000054$ is $5.4$
and
it is necessary to move the decimal point $7$ positions to the left from $5.4$ to get the actual value; there fore the "exponent" portion is ${10}^{- 7}$