To multiply decimals, first ignore the decimal point.
For example: 5.3 x 4.2 = 22.26 on a calculator.
To manually reach the same answer:
Multiply without the decimal point: 53 x 42 = 2226
5.3 is 1 decimal point
4.2 is 1 decimal
Total is 2 decimal points, which makes the answer 22.26
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By the time you advance to the point of dividing decimals, you don't use remainders any more.
Using an estimate ensures that the answer is about right. With decimals where the decimal point should go is difficult for a lot of people, so an estimate of the answer ensures that it is put in the right place.
When it dont work An easy solution is to move both decimal places (by the same amount of course) until there is no decimal places left. eg. .0045/.000046 is the same as 4500/46. and then just proceed normally.
To convert a decimal to a fraction first put the decimal over 1 as to divide the decimal by 1. Next multiply the top and bottom by 10 for every number after the decimal point. Finally simplify the fraction.
The bar is only used for repeating decimals. If it is repeating, you can use it.