🍫 Fraction, Decimal, Percentage: One Part, Three Names

Hello! We can write half a chocolate bar as 1/2, 0.5 or 50%. All three are names for the same part! Today we will learn about fractions, decimals and percentages together.

The hundred square has 100 small squares. We shaded 50 squares: exactly half! As a fraction that is 50/100 = 1/2, as a decimal 0.5, as a percentage 50%. A percentage tells us how many parts we have when we cut a whole into 100 equal parts.

The chocolate bar is cut into 4 equal parts, and we took 1 part: 1/4. On the hundred square that is 25 squares: 25/100. As a decimal it is 0.25, as a percentage 25%.

This time we cut the square into 10 equal columns and shaded 3 columns: 3/10. That is 30 squares: 30/100. As a decimal it is 0.3, as a percentage 30%. The first digit after the decimal point is the tenths place. 0.3 and 0.30 are the same number.

Now let’s shade just 7 squares: 7/100. As a decimal it is 0.07, as a percentage 7%. The second digit after the decimal point is the hundredths place. Careful: 0.7 is a different number. It is 7/10, which is 70%.

Now let’s look at the number line. Between 0 and 1 there are 10 equal parts. Each part is 1/10, which is 0.1 or 10%. The third mark: 3/10 = 0.3 = 30%. The mark in the middle: 1/2 = 0.5 = 50%. At the far right: 1 = 100%, the whole.

Let’s zoom in on the small parts. The space between 0.2 and 0.3 is cut into 10 equal parts too: these are hundredths. Exactly halfway is 0.25. 0.25 = 25/100 = 25% = 1/4.

A percentage shows how much of the bar is full. When a quarter of the bar is full it is 25%, half full is 50%, three quarters full is 75%, and completely full is 100%. Each one has a decimal and a fraction name too: 0.25 and 1/4; 0.5 and 1/2; 0.75 and 3/4; 1.

To change a fraction into a percentage, let’s make the denominator 100. Take 3/5: the denominator is 5, and 5 × 20 = 100. We multiply the numerator by 20 too: 3 × 20 = 60. So 3/5 = 60/100 = 0.6 = 60%. The shaded parts of both bars are the same length!

Summary: One part has three names: a fraction, a decimal and a percentage. 1/2 = 0.5 = 50%, 1/4 = 0.25 = 25%, 3/10 = 0.3 = 30%. The hundred square and the number line make it easier. Now try it in Fraction Trail!