Decimal remainders

The decimal number 1.52 is read as one and fifty-two hundredths, or 1 Q. The number. 05 is read as five hundredths, or Decimal numbers are easy to compare and order, when you remember that the place value has meaning. In mathematics, 2.4 is the same number as 2.400 because both numbers represent two and four tenths. A whole number is understood to have a decimal point to the right of the number. For example, 12 = 12. = 12.0 = 12.000. Each expression represents twelve with no remainder. To compare decimals, it is best to change each decimal into an equivalent decimal with the same number of decimal places. 

Pete has to put one dozen doughnuts in each box. It takes 12 donuts to make a dozen. Divide 4,000 by 12 and determine the remainder — if there is one 4,000 + 12 = 333 with 4 left over. The owner of the shop has 333 boxes of donuts to sell, and Pete gets the last 4. This is a case where it didn t make sense to change the remainder to a fraction or decimal. The last four doughnuts weren t going to be sold — but the number of doughnuts remaining was pretty important to Pete ... 

The 480 pounds of candy divided into 100 smaller units doesn t come out to a whole number of pounds of candy in smaller boxes. Chuck changes the remainder into a fraction and uses it in determining the cost of each small box. To answer the question, you don t need to know the cost per pound — that s just extra information needed by Chuck. Just do the division 480 100 = 4 with a remainder of 80. Change the 80 to a fraction or decimal, and the result of the... 

The standard rule for rounding numbers is to round down when the fractional or decimal part is less than half (when the remainder is less than half of the divisor), round up when the fractional part is more than half, and round to the closer even number when the fractional part is exactly half. 

First, dividing 75 by 9, you get 8 with a remainder of 3. In decimals, this is 8.3. (That line over the 3 indicates that the number repeats forever.) It looks like Ebenezer just lopped off the remainder and kept it himself — because he paid in silver dollars and no other coins, he couldn t give his employees the fraction of the total. But if Ebenezer really wanted to be fair, he would multiply the 75 times the 12 months of the year to get 900. Dividing that by 9, each employee would get 100 dollars for the whole year instead of 96 dollars (8 x 12). He could give the extra as a holiday bonus. 

Fractions all have decimal values, but some of these decimals terminate (come to an end) and some repeat (never end). As long as the denominator of the fraction is the product of 2s and 5s and nothing else, then the decimal equivalent of the fraction will terminate. To find this terminating decimal, you divide the denominator (bottom) of the fraction into the numerator (top) and keep dividing until there s no remainder. You may have to keep adding 0s in the divisor for a while, but the division will end. 

How do you get the 8Long division gives you a remainder of 8into fractions automatically. 

As shown above, total 16 digits are used in hexadecimal system. While converting decimal number to hexadecimal number, we divide decimal number by 16 unless we get remainder less than 16 because the base of hexadecimal system is 16. This can be understood by the following problem. 

Just as when we divide a whole number by a whole number, there is often a remainder. When we divide a whole number by a whole number and there is a remainder, we add a decimal point to the dividend followed by a zero. We continue adding zeros until we are done dividing. When the dividend already has a decimal point, we just add zeros until we are done dividing. 

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