There are plenty of instruments out there that don't have unit rods marked on the beam. The following
techniques are one solution to solving the question, "Where should the decimal point go?"

MULTIPLICATION:

**Rule:** Simplify both numbers to read x.xxx... Take the net of the decimal point movement in both the
multiplicand and in the multiplier. (This yields a number.) In the final analysis, undo by that number by
moving in the opposite direction. This is probably best explained in the following examples:

**Example 1:** 31.68 x 0.00082

Put both numbers in the form x.xxx .....

Move the decimal in the multiplicand one place to the left (call it **L1**).

Move the decimal in the multiplier four places to the right (call it **R4**).

This gives : 3.168 x 8.2

Take the net of these : **L1** plus **R4** = **R3.**

In the final analysis remember to *undo* **R3** by moving the decimal point **L3**.

Now, look again at the equation : The approximation is 3 x 8 = 24

Undo **R3** by moving the decimal point **L3**. This leaves 0.024

The actual answer to the problem is : 31.68 x 0.00082 = 0.0259776

**Example 2:** 5326.879 x 0.00000079

Put both numbers in the form x.xxx .....

Think : **L3** for the multiplicand and **R7** for the multiplier

5.326879 x 7.9

Take the net of these : **L3** plus **R7** = **R4**

Remember to "undo" **R4** at the end by moving the decimal point **L4**.

The approx answer is 5 x 8 = 40

Undo **R4 **by moving the decimal point **L4**. This leaves 0.0040

The actual answer to to the problem is : 5326.879 x 0.00000079 = 0.004208234

DIVISION:

Here's a method to consider for locating the decimal point in problems of division. The method is similar to that done for problems of multiplication in that we simplify both numbers to read x.xxx.... However, it's a little more complicated but once gotten used to it's very easy.

**Rule:** Simplify both numbers to read x.xxx... Take the net of the decimal point movement in the dividend and
the **opposite** of the decimal point movement in the divisor. (This yields a number.) In the final analysis,
undo by that number by moving in the opposite direction. Probably best explained by example. :)

**Example 1**: 0.68 ÷ 390

Put both numbers in the form x.xxx .....

Move the decimal in the dividend one place to the right (call it **R1**)

Move the decimal in the divisor two places to the left (call it **L2**)

The result is : 6.8 ÷ 3.9

Take the net of the decimal movement in the dividend and the **opposite** of the movement in the divisor. That
is;

**R1** plus **R2** = **R3**

6.8 ÷ 3.9 is approximately 7 ÷ 4 = 1.75

Undo **R3** by moving the decimal **L3** : this equals 0.00175

The actual solution : 0.68 ÷ 390, is 0.00174358

**Example 2:** 0.073 ÷ 0.0054

Put both numbers in the form x.xxx .....

Think : **R2 **for the dividend and **R3** for the divisor

The result is : 7.3 ÷ 5.4.

Take the net of the decimal movement in the dividend and the **opposite** of the movement in the divisor. That
is;

**R2** plus **L3** = **L1**

7.3 ÷ 5.4 is approximately 7 ÷ 5 = 1.4

Undo **L1** by moving the decimal **R1** : this equals 14.00

Actual solution : 0.073 ÷ .0054 = 13.518...

**Example 3:** 897 ÷ 0.00061

Put both numbers in the form x.xxx .....

Think : **L2** for the dividend and **R4** for the divisor

8.97 ÷ 6.1

Take the net of the decimal movement in the dividend and the **opposite** of the movement in divisor. That is;

**L2** plus **L4** = **L6**

8.97 ÷ 6.1 is approximately 9 ÷ 6 = 1.5

Undo **L6** by moving the decimal** R6** : this equals 1500000.00

Actual solution : 897 ÷ 0.00061 = 1470491.803

*Back to Multiplication*

*Back to Division*

*Back to Finding the Decimal*

Gary Flom Atlanta Georgia USA

Email

gsflom[at]bellsouth[dot]net