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Compare Integers and Decimal Numbers.

Compare Integers and Decimal Numbers.

The decimal notation is very useful to compare numbers, as soon as we are able to order the 10 digits from 0 to 9: 0<1<2<3<4<5<6<7<8<9.

To know which number is the greatest between 2 natural integers a≥0 and b≥0, we first compare the number of digits of a and b. If a has more digits than b, then a>b, and reversely. For instance 96<456 and 16>0.

If a and b have the same number of digits, then we compare the digits that are the most to the left. If they are different, then the greatest number is the one that has the highest left digit. For instance 456>196 and 73<88.

If the left digits are the same, we compare the next digits to the right, with the same rule as for the left digits. For instance, 456<465.

If the two first digits to the left are the same, then we compare the third digits, wit the same rule. For instance, 456<458.

We continue that way until we arrive to distinct digits, which happens because the numbers are supposed to be different…

Now, to compare decimal numbers, with at least one with a decimal point, we first compare the numbers before the decimal point, the integer parts. If they are different, the biggest number is the one with the greatest integer part. For instance, 4.5>2.

If two decimal numbers have the same integer part, we compare the first digits after the decimal points, that may be 0. For instance, 4.5>4.4 and 2.1>2.

We continue to compare the digits after the decimal points until we find 2 of them being differents, that digit possibly non-existent thus being 0. For instance, 3.45<3.46 and 3.45<3.451.

If all the digits are the same, then the numbers are equal. It is the same if there are às at the end of a number completing the digits of the other number. For instance, 0.50=0.5.

That's why taking 50% of an amount, that is multiplying by 0.50, is also multiplying by 0.5=1/2 or dividing by 2!

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