I. Precision of the result
When we carry out a decimal division, we can ask to how many decimal places of the quotient should be worked out.
If the instructions in the problem are of the sort “give the decimals for the quotient up to the hundredth,” then there is no ambiguity. If this is not the case, then what do we do?
It all depends on what we want to use the quotient for. If, for example, we are carrying out a decimal division to calculate a price in dollars, then it is enough to stop at the hundredths; if we need to calculate a length in centimeters, we can stop at the tenths (a tenth of a centimeter is a millimeter), etc.
II. First example of decimal division
We can start with an example to describe the stages of the calculation: We want to find the quotient of the division of 43.7 by 8.
How many times does 8 go into 43? 5 times.
5 × 8 = 40; 43 – 3 = 3
We place a decimal point in the quotient. We move the 7 down.
How many times does 8 go into 37? 4 times.
4 × 8 = 32; 37 – 32 = 5
We move down a zero.
How many times does 8 go into 50? 6 times.
6 × 8 = 48; 50 – 48 = 2
We move down a zero.
We continue like this until the remainder is equal to zero.
Thus we obtain: 43.7 ÷ 8 = 5.4625.
III. Second example of decimal division
It is always possible to transform the division of a decimal number by a whole number into the division of a whole number by another whole number. Thus, to carry out the decimal division of 43.7 by 8 is the same as to carry out the division of 437 by 80. Why?
Because
Reading and Writing Decimal Numbers
Multiplying or Dividing a Decimal Number by 10, 100, or 1,000
Multiplying Decimal Numbers
Converting Decimals to Fractions
The Effect of Addition and Multiplication on the Order of Numbers
Describing Different Types of Numbers
Dividing Whole Numbers with a Remainder
Comparing and Ordering Decimal Numbers
Adding and Subtracting Decimal Numbers