Multiplication Of A Decimal Fraction By A Decimal Fraction -
We have to write the numbers in column form. Then we have to multiply the multiplicand with the multiplier as in common multiplication. But it is important to know where to put the decimal point in the product. The number of decimal places in the product is equal to the total number of decimal places in the multiplicand and the multiplier together.
1) Find the product:
a) 18.4 × 0.12
1 8 . 4
× 0 . 1 2
---------------------------
3 6 8
+1 8 4 ×
0 0 0 ×
-------------------------------
0 2 . 2 0 8
[As the multiplicand 18.4 has one decimal place and the multiplier 0.12 has two decimal places so the product 2.208 has three (1 + 2) decimal places.]
.: Answer is 2.208 (Ans.)
b) 0.004 × 0.064
0 . 0 0 4
× 0 . 0 6 4
---------------------------------
0 0 1 6
0 0 2 4 ×
+0 0 0 0 × ×
--------------------------------------------
. 0 0 0 2 5 6
[As the multiplicand 0.004 has three decimal places and the multiplier 0.064 has three decimal places so the product 0.000256 has six (3 + 3) decimal places.]
.: Answer is 0.000256 (Ans.)
g) 3.48 × 16 × 0.5
In this sum the first number is a decimal fraction, the second number is a whole number and the third number is again a decimal fraction. In Step 1 we multiply the first number with the second number. And in Step 2 we multiply the answer of Step 1 with the third number.
Step 1 Step 2
3 . 4 8 5 5 . 6 8
× 1 6 × 0 . 5
-------------------- -----------------------
2 0 8 8 2 7 . 8 4 0
+ 3 4 8 ×
----------------------
5 5 . 6 8
[In Step 1 a decimal fraction is multiplied by a whole number, so since the multiplicand 3.48 has two decimal places so the product 55.68 also have two decimal places. In Step 2 a decimal fraction is multiplied with another decimal fraction, so since the multiplicand 55.68 has two decimal places and the multiplier 0.5 has one decimal place so the product 27.840 has three (2 + 1) decimal places. 27.840 = 27.84 as removing zeroes from the extreme right of the decimal point does not change the value of the number.]
.: Answer is 27.840 = 27.84 (Ans.)