Question

Shade the given percent of a 100 -grid. Then express the shaded portion as a fraction and a decimal. $$4 \%$$

Short answer

Shade 4 squares, \[ \frac{4}{100} = \frac{1}{25} \, and 0.04.

Step-by-step solution

- Understand the Percent

4% means 4 out of 100 parts. To shade a 100-grid, you'll be shading 4 of those parts.

- Shade the Grid

Take the 100-grid, which consists of 10 rows and 10 columns, and shade 4 squares. These shaded squares represent the 4%.

- Express as a Fraction

The shaded portion is 4 out of 100, which can be expressed as a fraction: \[ \frac{4}{100} \]

- Simplify the Fraction

Simplify \[ \frac{4}{100} \] by dividing the numerator and the denominator by their greatest common divisor (4), resulting in \[ \frac{1}{25} \]

- Convert to a Decimal

To convert the fraction \[ \frac{4}{100} \] to a decimal, divide 4 by 100: \[ 4 \div 100 = 0.04 \]

Key concepts

Percent

A percent represents a part out of 100. When we say '4%', it means 4 out of 100 parts. This makes it very easy to visualize using a 100-grid. Imagine a 10x10 grid; each small square represents 1% of the entire grid. To visualize 4%, you shade 4 of these 100 small squares. Understanding percentages as parts per hundred helps in comparing different values easily. For example, 50% of the grid would mean shading half of it, or 50 squares.

Fraction Simplification

Expressing a percent as a fraction is straightforward. For 4%, you start with the fraction \[ \frac{4}{100} \]. To simplify this fraction, we need to reduce it by finding the greatest common divisor (GCD) of the numerator and the denominator. In this case, the greatest common divisor of 4 and 100 is 4.

We divide both the numerator and the denominator by 4:

• Numerator: \[ 4 \div 4 = 1 \]
• Denominator: \[ 100 \div 4 = 25 \]

Thus, the simplified fraction is \[ \frac{1}{25} \]

Fraction simplification helps in making calculations easier and results more understandable.

Decimal Conversion

Converting a fraction to a decimal is another way of representing the same value. To convert the fraction \[ \frac{4}{100} \] to a decimal, you simply divide the numerator by the denominator. In this case, you divide 4 by 100:

• 4 divided by 100 equals 0.04

The result is 0.04, which is the decimal form of 4%.

This method works for any fraction. For example, if you are converting \[ \frac{1}{4} \] to a decimal, you divide 1 by 4, getting 0.25. Decimals are often easier to use in further calculations, especially in scientific and financial contexts.