2.02 Percents as decimals

Let's use the same visual representations we used for comparing fractions and percents to explore the relationship between decimals and percents.

\\\\\\\,\\\\\,\\\\In a 10 \times 10 grid, each box represents 0.01.

Since 14 boxes are shaded, this model represents 14 \% or 0.14.

We could also write as a fraction: \dfrac{14}{100} = \dfrac{7}{50}

Double number lines can be helpful to model equivalencies between percents and decimals. Bechmark percents and decimals can make problem solving more efficient.

We can convert between decimals and percentages by taking advantage of the hundredths place value. We know that 1\% represents \dfrac{1}{100}, or 1 hundredth, which we can write in decimal form as 0.01.

We can convert any percentage into a decimal by dividing the percentage value by 100, which is equivalent to decreasing the place value of each digit by two places, and removing the \% symbol.

For example, 83\% = \dfrac{83}{100} which can be described as 83 hundredths. This is also 0.83 when written as a decimal.

To convert from a decimal into a percentage, we can just reverse the above steps. We can convert any decimal into a percentage by multiplying the decimal by 100, which is equivalent to increasing the place value of each digit by two places, and attaching a \% symbol.

For example, 0.08 is 8 hundredths or \dfrac{8}{100}=8\%.

A percentage is limited to representing hundredths, so smaller units like thousandths cannot be represented by whole number percentages such as 0.0035 which is 0.35\%.

Remember to attach the \% symbol to decimal at the same time as increasing the place values.

Examples

Example 1

Write 54\% as a decimal.

Worked Solution

Create a strategy

To convert a percentage as a decimal, we can first think of 54\% as 54 hundredths.

Apply the idea

54\% is \dfrac{54}{100} or 54 hundredths.

54 hundredths can be written as a decimal as 0.54

Reflect and check

Let's use a 10\times10 grid to illustrate converting 54\% to decimal.

The grid represents a whole. Since there are 100 squares, each square represents 1\% or 0.01.

Adding the 54 shaded squares that each represent 0.01 gives us 0.54, which confirms our original conversion of 54 \% to a fraction.

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Example 2

Write 0.314 as a percentage.

Worked Solution

Create a strategy

To write a decimal as a percentage multiply by 100 and add the \% symbol.

Apply the idea

\displaystyle 0.314 \cdot 100	\displaystyle =	\displaystyle 31.4	Multiply by 100
	\displaystyle =	\displaystyle 31.4\%	Add the \% symbol

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