Operations on Decimal Fractions 2

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Multiplication 

The example given below will clarify the principle involved.

The procedure can be further simplified into
 * 1) We multiply each of the numbers with suitable powers of ten, so that they become whole numbers.     245.45 is multiplied by 100 or 10^2 &amp; 365.898 is multiplied by 1000 or 10^3. Notice that the power of each 10 is equal to the number of effective decimal places in the number.Hence the product has been multiplied by 100 X 1000 or 10^5. This again is equal to the sum of the decimal places of the individual numbers.It is very easy to see that 10^2 X 10^3 = 10^(2+3) by the rule of multiplication of exponentials
 * 2) The product of multiplication is 8980966410
 * 3) We now divide this by 10^5. This is easy because of the place value notation and means shifting the decimal point to the left by 5 places.
 * 4) Hence 8980966410 converts to 89809.66410

Treatment of 0 at the right extreme in any of the numbers being multiplied
 * 1) Find the total of the decimal places of each number.
 * 2) Multiply both the numbers, ignoring the decimal point.
 * 3) Shift the decimal point to the left as many places as the total arrived at in Step 1.

If the decimal places in a number take into account 0s on the right, then the whole number should retain the 0s.

Treatment of 0 at the right extreme of the product
 * 1) If the decimal places in 245.450 are taken as 3, then the whole number equivalent should be taken as 245450.
 * 2) If the decimal places in 245.450 are taken as 2 (taking the number as 245.45, then the whole number equivalent should be taken as 24545.

In the same example we saw that the product had a 0 in the right extreme. Since the product is a whole number, the 0 cannot be disturbed. Hence while shifting the decimal point 5 places to the left, the 0 was counted as one of the places.

After shifting the decimal point (since it is now a decimal fraction) the trailing 0s can be left out.

Hence 89809.66410 could be written as 89809.6641

Division

The Divisor and the Dividend are multiplied by a suitable power of 10, so that at least the Divisor becomes a whole number. Since both are multiplied by the same number, the result is not affected. Then the problem reduces to that of dividing either a whole number or a decimal fraction by another whole number.

The procedure is same as division of a whole number by another whole number. The decimal point is placed appropriately in the quotient also

Improving Decimal Number Sense

If 346 X 228 = 78888 write at least 4 different problems (with the same numbers) with both the factors having different number of decimal places. For example what is 3.46 X 22.8?

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