Fractions and decimals for KS4

In this material, we will take a closer look at how fractions are written in decimal forms and vice versa.

A decimal fraction is a fraction with a denominator that is a multiple of the number 10 but instead of writing them as fractions, we use decimals to represent parts of a whole.

Each digit in a decimal number has a specific place value, which determines its value:

Rational fractions are fractions where both the numerator and the denominator are integers. In simpler terms, they represent a part of a whole number. It should also be noted that rational fractions can also be expressed as decimal fractions.

Any rational number in decimal form can be written as a fraction. This is done by first writing the number as a decimal fraction, and then simplify the resulting fraction to its simplest form.

In this section, we will deal with fractions with a denominator that is not a multiple of the number 10.

Recurring decimals, also known as repeating decimals, are decimal numbers that have a repeating pattern of digits.

Not all fractions are decimal and such fractions cannot be extended so that the denominator becomes a multiple of the number 10. These fractions are regarded as non-decimal fractions.

If we attempt to write non-decimal fractions as a decimal number, we would have infinite decimals otherwise called recurring decimals.

The notation of a decimal number with infinite decimals is long and inaccurate. Decimal numbers with a recurring periods are called recurring decimal numbers and period is the number that is repeated in the decimal notation. The decimal notation can thus be shortened with a horizontal line above the period, thus illustrating the repetition of the period.

Finally it should be noted that:

Each recurring decimals can be written as a fraction. We will show the procedure on how to do so in the following example.

In this section, we will look at addition, subtraction, multiplication, and division of decimal numbers.

To obtain the solution for addition and subtraction of decimals, we first write the two decimals given one below the other such that one decimal point is below the other decimal point and then calculate the equivalent digits as shown below :

To multiply two decimal numbers, we first simplify the products and initially neglect the decimal point. Finally, the decimal places of each of the decimal number would be added and this would determine where to place our decimal point.

It would be noted that the two decimal numbers given in this task are in one decimal place and two decimal place respectively and the sum of one and two gives three, hence, our result is in three decimal places.