Understanding Decimals
Decimals are an essential part of mathematics, bridging the gap between whole numbers and fractions. A solid grasp of decimal place value is crucial for mastering more complex mathematical concepts. This lesson will introduce you to decimals, their place value, and how they relate to fractions.
Introduction to Decimals Quiz
What is a Decimal?
The term "decimal" comes from the prefix "deci," which means one-tenth. Therefore, one decimal place represents a division by ten. Formally, a decimal is a number that includes a whole number and/or a fraction, expressed using powers of ten as the denominator. For example, 1 10 equals 0.1.It could be any of the followings:
- Just a whole number with decimal places (e.g., 5.0)
- Just a fraction less than 1 (e.g., 0.25)
- A combination of both (e.g., 5.25)
For example:
0.5 is a decimal (no whole number part)
3.0 is a decimal (no fractional part)
3.14 is a decimal (has both parts)
In general, decimals can represent any proper or improper fraction where the denominator is a power of ten, such as 10, 100, 1000, and so on. This structure allows for precise representation of values between whole numbers.
Decimal Place Value
Understanding the place value of each digit in a decimal is fundamental. Each position to the right of the decimal point represents a power of ten.
- The first position to the right of the decimal point is the tenths place (10-1) as shown in 0.5.
- The second position to the right of the decimal point is the hundredths place (10-2) as in 0.02.
- The third position to the right of the decimal point is the thousandths place (10-3) as shown with the 9 in 0.0195
2 100 = 0.02
16 1000 = 0.016
1 100 = 0.01
195 10000 = 0.0195
45 10 = 4.5
234 100 = 2.34
Notice that the first five examples are proper fractions, where the numerator is less than the denominator, resulting in a decimal less than one. The last two are improper fractions, where the numerator is greater than the denominator, resulting in a decimal greater than or equal to one.
A Few Important Terminology to Keep in Mind about the Decimals.
- A proper fraction whose denominator can be written as a power of 10 is called a decimal fraction. 5 10 = 0.5 and 16 1000 = 0.016 are examples of decimal fractions.
- An improper fraction whose denominator can be written as a power of 10 is called a mixed decimal. 45 10 = 4.5 and 234 100 = 2.34 are examples of mixed decimals.
- We can say that a decimal is a combination of a whole number and a fraction of a whole number.
- Notice also that a whole number is also a decimal. For example, 69 can also be written as 69.0 since 69 = 69.0.
The Relationship Between Decimals and Fractions
Decimals and fractions are two different ways of representing parts of a whole. Decimals are particularly useful in measurements and financial calculations due to their precision and ease of use in addition and subtraction. Understanding how to convert between fractions and decimals is a valuable skill:
Converting Fractions to Decimals: Divide the numerator by the denominator. For example, 5 10 = 5 ÷ 10 = 0.5 Converting Decimals to Fractions: Write the decimal over its place value and simplify if possible. For example, 0.016 = 16 1000