Introduction to Decimals Study Guide
Introduction to Introduction to Decimals
The highest form of pure thought is in mathematics.
—PLATO, classical Greek philosopher (427 B.C.E.–347 B.C.E.)
The first decimal lesson is an introduction to the concept of decimals. It explains the relationship between decimals and fractions, teaches you how to compare decimals, and gives you a tool called rounding for estimating decimals.
A decimal is a special kind of fraction. You use decimals every day when you deal with measurements or money. For instance, $10.35 is a decimal that represents 10 dollars and 35 cents. The decimal point separates the dollars from the cents. Because there are 100 cents in one dollar, 1¢ is of a dollar, or $0.01; 10¢ is of a dollar, or $0.10; 25¢ is of a dollar, or $0.25; and so forth. In terms of measurements, a weather report might indicate that 2.7 inches of rain fell in 4 hours, you might drive 5.8 miles to the intersection of the highway, or the population of the United States might be estimated to grow to 374.3 million people by a certain year.
If there are digits on both sides of the decimal point, like 6.17, the number is called a mixed decimal; its value is always greater than 1. In fact, the value of 6.17 is a bit more than 6. If there are digits only to the right of the decimal point, like .17, the number is called a decimal; its value is always less than 1. Sometimes these decimals are written with a zero in front of the decimal point, like 0.17, to make the number easier to read. A whole number, like 6, is understood to have a decimal point at its right (6.).
Each decimal digit to the right of the decimal point has a special name. Here are the first four:
The digits have these names for a very special reason: The names reflect their fraction equivalents.
0.1 = 1 tenth =
0.02 = 2 hundredths =
0.003 = 3 thousandths =
0.0004 = 4 ten thousandths =
As you can see, decimal names are ordered by multiples of 10: 10ths, 100ths, 1,000ths, 10,000ths, 100,000ths, 1,000,000ths, etc. Be careful not to confuse decimal names with whole number names, which are very similar (tens, hundreds, thousands, etc.). The naming difference can be seen in the ths, which are used only for decimal digits.
Reading a Decimal
Here's how to read a mixed decimal, for example, 6.017:
|1.||The number to the left of the decimal point is a whole number. Just read that number as you normally would:||6|
|2.||Say the word "and" for the decimal point:||and|
|3.||The number to the right of the decimal point is the decimal value. Just read it:||17|
|4.||The number of places to the right of the decimal point tells you the decimal's name. In this case, there are three places:||thousandths|
Thus, 6.017 is read as six and seventeen thousandths, and its fraction equivalent is .
Here's how to read a decimal, for example, 0.28:
|1.||Read the number to the right of the decimal point:||28|
|2.||The number of places to the right of the decimal point tells you the decimal's name. In this case, there are two places:||hundredths|
Thus, 0.28 (or .28) is read as twenty-eight hundredths, and its fraction equivalent is . You could also read 0.28 as point two eight, but it doesn't quite have the same intellectual impact as 28 hundredths!