Table of Contents
What is Meant By a Decimal?
A decimal is a number expressed in the base-10 number system, using the digits 0 through 9. The number 10 is the base, and the digits in a decimal represent successive powers of 10. For example, the decimal number 123.45 is equal to 1×10² + 2×10¹ + 3×10⁰ + 4×10⁻¹ + 5×10⁻².
How is Decimal Related to Fractions?
A fraction is a representation of a decimal number where the numerator (top number) is the number of whole units that are being divided and the denominator (bottom number) is the number of units that are left over. For example, the fraction ¾ can be represented as the decimal .75. This means that there are three whole units and three-quarters of a unit left over.
Terminating Decimal Numbers
Terminating decimal numbers are those that have a finite number of digits after the decimal point. For instance, the number 0.14 has 14 digits after the decimal point, while the number 0.0005 has only 5 digits after the decimal point.
Terminating decimal numbers can be represented in scientific notation as follows:
0.14 = 1.4 x 10-2
0.0005 = 5.0 x 10-5
Non-terminating Decimal Numbers
A decimal number that does not terminate is called a non-terminating decimal number. Non-terminating decimal numbers can be represented in two ways: as a fraction, or as a recurring decimal.
A fraction is a number that is written as a fraction of two integers. The numerator is the top number in the fraction, and the denominator is the bottom number. In a fraction, the number of digits that appear in the numerator is always larger than the number of digits that appear in the denominator. For example, the fraction 2/3 has two digits in the numerator (2) and three digits in the denominator (3).
A recurring decimal is a decimal number that repeats a certain pattern of digits. For example, the decimal number 0.333… (pronounced “zero point three three three repeating”) repeats the pattern “3” over and over again.
Recurring Decimal Number
A decimal number that is repeated in a pattern. For example, the recurring decimal number 0.142857142857142857… can be represented as the fraction 1/7.
Ultimately Period Decimal Numbers
Period decimal numbers are numbers that are written as a decimal number, followed by a period and then one or more digits. Period decimal numbers can be used to represent any quantity that can be measured in units of tenths, hundredths, thousandths, or millionths.
How are Decimal Worksheets Related to Fractions?
Decimal worksheets are related to fractions because fractions are a way of expressing a decimal value. For example, the decimal value 0.75 can be expressed as the fraction 3/4.
