For example, when expressing a measurement, when specifying amounts in an inventory, or amounts of an ingredient - depending on the unit used. For instance, when measuring the length of something fairly small, you might use millimeters and use integers; or you might use meters and use three decimals instead. Note that for some calculations you might need to convert all measurements to meters, for example. For a more specific example, I was in charge of a computer program that handled the inventory of a company; the amounts of materials delivered allowed four decimal digits, which I found to be enough for our purposes. Similarly, the computer program also made cost calculations - the amount of different materials used to make an item had to be specified; once again, we used four decimals.
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The first people to use the decimal system and the number zero WERE NOT THE CHINESE! I am learning about this in school. The ancient Hindu's invented them during the Gupta Empire.
how can you use expanded notation to find an equivalent decimal
everywhere
You would use two number 1's and a decimal point. It would be written as 1.1
Most people use 1/12 and multiply that by the number of months to get their decimal age. HOWEVER this is not exact because you are often a fraction of a month old, AND not all months are the same length. To figure out your age to an exact decimal, first add up the days until your next b-day (example: if today is April 27th and my b-day is July 10th, I would add 3 days + 31 days + 30 days + 10 days). Now, divide that number by 365. Write down the decimal you get. Now, do 1 - (the decimal you wrote down). You will get another decimal. Just add your age in years, and you have your decimal age! *This is fun because afterwards you get to brag, "I'm 17.7392649092739... years old!* Note: Use a calculator to make it easier! You can use memory on your calculator for the part where you subtract the decimal from 1.