What does period mean in math?
Period, in general means, a part or a portion of time or length. What does period mean in math? Period, in math is used in a number of ways such as a period in place value of a number or a period of a sine function and so on. Let us learn some more about the use of the period in math.
A period in Place Value
Place value is a system that defines the value of a digit according to its position in a number. We read a number from right to left, starting with ones, tens, hundreds etc. A set of positions in a place value is combined into a period and each period is separated by a comma. The following is the representation of a place value chart according to the International Place Value System –
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We can see from above that ones, tens and hundreds together constitute one period. This period is called “ Ones ”. Similarly, thousands, ten thousands and hundred thousand constitute one period. This period is called “ Thousands ”. Millions, Ten million and a hundred million constitute one period. This period is called “ Millions “. Billion, ten billion and hundred billion constitute one period. This period is called “ Billions “.
Example 1
Using periods, write the place value of the number 2910770403. Also, write the obtained number in words.
Solution 1
We have been given the number 2910770403. Using the rules defined above; starting from the right, let us place a comma after every three digits. We will have
2910770403 = 2,910,770,403
The obtained number in words would be “ Two billion nine hundred and ten million seven hundred and seventy thousand four hundred and three “.
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Period of Decimal Numbers
A decimal number can have digits that are repeating, known as recurring decimals or digits that are not being repeated, known as non-recurring decimals. The digits that are repeated constitute a decimal period.
For example, the fraction 1 / 3 when written in decimals will be 0.3333333….. We can see that it is a recurring decimal with the digit 3 being repeated infinitely. Therefore, the decimal period of the fraction 1 / 3 will be 1 as there is one number that repeats itself and the number will be written as 0. 3 ̅. The bar above the digit 3 represents the decimal period of the number.
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Period of a Function
When defining periodic functions, the time period is the length between the peak of one point to the peak of the next point. This is particularly of relevance in the case of trigonometric functions. These functions are known as periodic functions.
The time period of function means that the values of the function are repeated after every time period of the function. Let us check the time period of the sine and cosine functions.
Sine Function
The sine function is a periodic function having a time period of 2π. This means that the values of the sine function are repeated after every 2π. The following is the graph of the sine function –
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Let us take an example.
Example 2
If sin ( π) = 0, what will be the value of sin 3π?
Solution 2
We have been given that sin ( π ) = 0. We know that the time period of the sine function is 2π. Therefore, we can write sin 3π as –
sin 3π = sin ( 2π + π ) = sin π = 0
Hence sin 3π = 0
Cosine Function
The cosine function, also known as the cos function is a periodic function having a time period of 2π. This means that the values of the cosine function are repeated after every 2π. The following is the graph of the cosine function –
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Let us take an example.
Example 2
If sin ( π) = 0, what will be the value of sin 3π?
Solution 2
We have been given that sin ( π ) = 0. We know that the time period of the sine function is 2π. Therefore, we can write sin 3π as –
sin 3π = sin ( 2π + π ) = sin π = 0
Hence sin 3π = 0
We have discussed two trigonometric functions above which have the same time period. Does that mean that their graphs are also the same? Let us observe their graphs –
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We can see above that the graphs of the sine and cosine functions are different. Hence, even if the time period of the two functions is the same, it does not mean that they have the same graphs.
What does Period Mean in Math? FAQs
Period means dividing values or time into certain groups. For example, numbers are divided into groups depending upon their place value.
Period in math examples, include dividing a number into groups depending upon the place of the digits of the number. For example, the number 431969 when divided into periods will be written as 431,969. It will be read as Four hundred thirty one thousand nine hundred and sixty nine.
In the international system of numeration, starting from the extreme every three digits form a period. For example, if we have a six digit number 196943 then it would be written as 196,943 and would be read as one hundred ninety six thousand nine hundred and forty three.
In the case of decimal numbers, the period of numbers start from the digits after the dot “ . “ and consists of the digits that are repeated.