# How do you express #0.0001/0.04020# as a decimal?

##### 4 Answers

#### Explanation:

Take

Use the "move the decimal" rule. ie.

If the goal was to covert the decimal directly to fractions and then solve, in

Multiply numerator and denominator by

#1/402 = 0.0bar(0)2487562189054726368159203980099bar(5)#

#### Explanation:

To calculate

Assuming we want a decimal expansion of the quotient, let's use long division.

First write out the multiples of

#0:color(white)(XX000)0#

#1:color(white)(XX0)402#

#2:color(white)(XX0)804#

#3:color(white)(XX)1206#

#4:color(white)(XX)1608#

#5:color(white)(XX)2010#

#6:color(white)(XX)2412#

#7:color(white)(XX)2814#

#8:color(white)(XX)3216#

#9:color(white)(XX)3618#

Then our long division starts:

Write the dividend

Bring down another

Notice that with the running remainder having arrived at

#1/402 = 0.0bar(0)2487562189054726368159203980099bar(5)#

I want to capitalize on George C. answer and give my version of

#### Explanation:

have a look:

Just for fun I thought I would add a solution as well. I am going to considerably limit the number of decimal places!!

#### Explanation:

Given:

Multiply the numerator by

so

Multiply the denominator by

Putting this all together gives:

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Write as:

Consider just the hundreds:

Do not worry about the remainder!

Now write:

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Now write:

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

subtract the 804 from the 1000

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~

402 > 196 so put a decimal place to the right of the 2 and put a

so

So now we write:

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

352 < 402 so put

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

So far we have 2.4. Applying the correction this becomes:

Look at the beginning to see where