Decimals represent parts of a whole number. Think of them as a way to show fractions using a dot (the decimal point) instead of a fraction bar. Each position after the decimal point represents a different fractional value.
Tenths, Hundredths, and Beyond
- Tenths Place: The first position after the decimal is called the tenths place. If you have the number 0.1, you’re looking at one-tenth.
- Hundredths Place: The next position is the hundredths place, as in 0.01, which means one-hundredth.
- Thousandths Place: After that is the thousandths place, like 0.001.
When you hear about statistics, the numbers are often precise. To show this precision, statisticians usually report numbers to at least the hundredths place. When a number is less than one, and there’s no whole number before the decimal, it’s standard to put a zero before the decimal. This 0 helps readers instantly realize they’re seeing a number smaller than one.
Fractions: Breaking Down the Basics
Fractions are another way to show parts of a whole, but they use a bar or slash instead of a decimal.
Expressing Fractions
- Traditional Fraction: This has a horizontal line. The number above the line is the numerator, and the one below is the denominator. For example, in the fraction 2/3, 2 is the numerator, and 3 is the denominator.
- Slash Division: This is similar but uses a slash, like 2/3.
From Fractions to Decimals
Fractions can be turned into decimals. By dividing the numerator by the denominator, we get a decimal form of the fraction, also known as a proportion.
How to Turn Proportions into Percentages
Multiplying a proportion by 100 changes it into a percentage. This is because “percent” means “out of 100.” So, moving the decimal point of a proportion two places to the right achieves this.
Examples:
- 2/3 equals approximately 0.6667, which is 66.67%.
- 1/2 is 0.5000, or 50.00%.
Key Points to Remember about Fractions:
- As the numerator grows, the fraction’s value grows.
- If the denominator grows, the fraction’s value shrinks.
- With complex fractions, make sure you do all the math for both the top and bottom before you divide.
Percentages: Making Comparisons Easier
A percentage is really just a special kind of fraction. The denominator is always 100. The term “percent” has its roots in the Latin phrase per centum, which means “by the hundred.”
Imagine saying 50% of people like apples. This is the same as saying 50 out of every 100 people you ask will like apples. Percentages make it easier to compare groups, no matter how big or small they are. This standardized way of understanding proportions helps us grasp big numbers or diverse groups.
How to Turn a Fraction into a Percentage
- Divide the numerator by the denominator.
- Multiply the result by 100.
By understanding decimals, fractions, and percentages, we can better interpret data and make informed decisions. They are essential tools in math and statistics.
Last Modified: 08/18/2023