 3 - Decimals

Decimals (or numbers with points)

Draw a line and place on it, at regular intervals, the numbers 0, 1, 2, 3, 4,... Question : Do there exist any numbers between 2 and 3?
Answer : The answer is yes, there are numbers between 2 and 3, namely numbers with points.

Below are positionned 9 numbers with points between 2 and 3. Numbers with points are also called "Decimals" whereas numbers without a point are called "natural numbers". New question : Now are there numbers between 2,6 and 2,7?
New answer : The answer is again yes. You must use two figures after the point. We can put as many numbers as we want between two numbers. Approximate numbers

When you do a division, the result is often a decimal number, with many figures after the point. For example, if you ask a calculator to calculate 20 divided by 3, the calculator displays 6,6666666666666... Since all the numbers are not necessarily useful, it is possible to approximate the result by writing only one or two figures after the point.

Example and Regular features :

To approximate 3,5973452 at 0,1 (1 figure after the point), you write down 3, you write down a point, then you approximate the following figure (5). In order to do that you can look at the next figure (9) : if this figure is smaller than 5 you approximate the result to 3.5 and if this figure is greater than or equal to 5, you approximate it to the number 3.6.

Train yourself!

What is the approximation at 0.001 of the number 7.92?

Calculation with Decimals

To add two Decimals you can write down the numbers ones under the others, lining up units, tens, ... and the points. Then to add the two numbers, you can use the technic seen in 2nd Grade. At last, you can write down a point and you can read the result. Same thing for subtraction. To multiply two Decimals, you can use the technic seen in 2nd Grade, but to place the point correctly in the final result, you must add the number of figures after the point of the 2 numbers you mutliply. In the example below, the first number has 2 figures after the point and the second number has one figure after the point thus the result will have 3 figures after the point. >>> Geometry lesson >>>

Decimals

problems