# How do you write 420,000 in scientific notation?

Mar 21, 2018

$4.2 \times {10}^{5}$

#### Explanation:

In scientific notation one number is written to the left of the decimal and the other significant digits written to the right of the decimal.

This gives 4.2

To keep the value of the numbers the same the significant digits must be multiplied by a power of ten

In this case ${10}^{5}$ The decimal point tmust be moved five places to the left

Mar 21, 2018

$4.2$ x ${10}^{5}$.

#### Explanation:

Scientific notation helps us write very small, or very large numbers so that they are understandable and more manageable.

How we start this is finding where the decimal is. In 420,000, the decimal place would be 420,000 .

Once we know that, we move the decimal place until the number is between 1 and 10 ( i.e. $1 < x < 10$ ).

When we do this, we count the number of times we move the decimal place. For 420,000, we move it 5 to the left.

Important note: if we move left, it will be a positive number, but if we move right it will be negative. (example: .00023 = -4 to the right)

Rewriting it with the moved decimal place, it would be 4.2. We cannot leave this alone, but there is another component we must add. We moved it 5 (positive) to the left, so this can be written as ${10}^{5}$. For scientific notation, the base of this is always 10.

Putting these all together, we can write it as:

$4.2$ x ${10}^{5}$

There is always a x, or multiplication, between the number and the base 10.