Sunday, 17 August 2008

How Many Decimal Places To Use?

A very common question maths student always ask is

"How many decimal places have I to use for this computing?".

This is not a simple question to answer.

Though the teacher may simply say "Use 3 decimal places" as a yardstick or to standardise marking or solutions, what is the underlying importance of selecting the correct amount of decimal places?

Many a times, the number of decimal places to be used in any mathematical calculation is not significant at elementary maths level. What is required at that education level is the understanding of the maths working or steps in solving the maths questions.

However, as we progress up the educational ladder, the importance or precision of the answer becomes significant.

Let us look at one example and its impact.

Example A: 2.143 has 2 parts.

  • 1st part is the integral portion of "2"

  • 2nd part is the 3 decimal places for "143" (after the decimal point).

Now let's divide the number 4 by the number in example A, and see the effect to the answer when we select various number of decimal places.

1) 4 / 2.143 = 1.867

2) 4 / 2.14 = 1.869

3) 4 / 2.1 = 1.905

What do you see in these results?

Not much changes right?

This is because the number divided "4" is too near or of the same unit as the divisor.

Let's change the number to be divided to 40.

1) 40 / 2.143 = 18.67

2) 40 / 2.143 = 18.69

3) 40 / 2.1 = 19.05

Do you notice that the difference got bigger?

What is the impact when the number to be divided increases to 400?

The differences will be drastic now!

400/ 2.143 = 186.7 and 400 /2.1 = 190.5, a difference of 3.8!

So what's the rationale in deciding the number of decimal places?

We need to understand the relative scale of all the numbers involved in the computation of the maths questions.

When the numbers involved are of the same scale, the number of decimal places is not an issue. However, when numbers are relatively bigger, more decimal places are required to have better precision to reflect an accurate answer.

In the last division, it may be a difference of 3.8 metre of length or $3.8 difference in monetary change!

Maths learning, thus, not only involves pure manual calculation, but also involves the logical interpretation of the steps and the impact of the numbers and their decimal placement.

The logical thinking part in maths education does places a significant benefit to anyone mastering maths in his future life, as he is able to decide and use the appropriate method and techniques to achieve results.


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