Fractions, Decimals and Percentages

Understanding the relationships between fractions, decimals, and percentages is crucial in mathematics. Each of these forms represents a part of a whole, but they are expressed differently.

• Fractions represent parts using a numerator and denominator (e.g., 1/2).

• Decimals represent parts as a division of whole numbers (e.g., 0.5).

• Percentages represent parts per hundred (e.g., 50%).

Converting between these forms is a valuable skill, as it enables clearer comparisons and calculations.

½ = 0.5 = 50%

¼ = 0.25 = 25%

¾ = 0.75 = 75%

1/3 = 0.333… = 33.33%

2/3 = 0.666… = 66.67%

5/2 = 2.5 = 250%

1/10 = 0.1 = 10%

2/10 = 0.2 = 20%

1/5 = 0.2 = 20%

2/5 = 0.4 = 40%

1/8 = 0.125 = 12.5%

3/8 = 0.375 = 37.5%

The more of these conversions you learn, the better - but for those who find it challenging, utilizing visual aids like pie charts or bar models can help in grasping the concepts more effectively.

Fraction divide Decimal x by 100 Percentage E.g. 7/20 is 7/20

Fraction The awkward one Decimal e.g. 0.35 × 100 divide by 100 Percentage

Converting decimals to fractions can be done by expressing the decimal as a fraction with a denominator of a power of ten. For example, to convert 0.75 to a fraction, we write it as 75/100, which simplifies to 3/4.

0.6 = 60/100, which can be simplified to 3/5.

0.78 = 78/100, which can be simplified to 39/50.

0.024 = 24/100, which can be simplified to 6/25.

1) Recurring decimals have the ability to express a fraction where the decimal representation repeats indefinitely; for example, 0.333… can be represented as 1/3.

2) The repeating part is usually marked with dots , also known as a vinculum, to indicate the sequence that continues indefinitely.

3) If there’s one dot, only one digit is repeated. If there are two dots, everything from the first dot to the second dot is the repeating bit. E.g. 0.3̅ represents 0.333…, where the 3 is the repeating digit, while 0.2̅5̅ signifies 0.252525…, with both 2 and 5 recurring.

4) You can convert a fraction to a recurring decimal:

EXAMPLE

Write 5/11 as a recurring decimal.

Just do the division, and look for the repeating pattern.

5/11 = 0.454545… so 5/11 = 0.45̅