EXPONENTS AND SCIENTIFIC NOTATION
About "Exponents and Scientific notation"
Here we are going to see, "Exponents and Scientific notation rules".
What is exponents?
The exponent of a number says how many times to use the number in a multiplication.
for example 5³ = 5 x 5 x 5
In words 5³ could be called as 5 to the power 3 or 5 cube.
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10² is called as 10 to the power 2 or simply called as 10 square. |
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10³ is called as 10 to the power 3 or simply called as 10 cube. |
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If we have 1/2 in the power, we can simply write the base inside the radical or square root. If we have 1/3 in the power,we can simply write the base inside the cube root |
How to move an exponents or powers to the other side ?
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If the power goes from one side of equal sign to the other side,it will flip.that is x = 4² |
The other names of exponent are index and power.
Basic Rules of Exponents and powers
Rule 1 :
Whenever we have to simplify two or more the terms which are multiplying with the same base,then we have to put the same base and add the powers.
Rule 2 :
Whenever we have two terms, which are diving with the same base,we have to put only one base and we have to subtract the powers.
Rule 3 :
Rule 4 :
Anything to the power zero is 1.
Rule 5 :
If we have same power for 2 or more terms which are multiplying or dividing,we have to apply the powers for every terms.Note:This rule is not applicable when two are more terms which are adding and subtracting.For example (x + y) ^m = (x^m + y^m) is not correct
Other things:
Point 1:
If we don't have any number in the power then we have to consider that there is 1
Point 2:
In case we have negative power for any fraction or any integer and if we want to make it as positive,we can write the power as positive and we should write its reciprocal only.
Scientific notation rules
A number is written is scientific notation when it is expressed in the form
To convert the given number into scientific notation, first we have identify where the decimal point and non zero digit come.
There are two cases in it.
Case 1 :
To move the decimal point to the left, we have to count number of digits as explained in the example given below.
According to the example given above, we have to move the decimal point 3 digits to the left and exponent of 10 should be 3 (positive integer)
When we do so, we get the scientific notation of the given number.
Hence, 2301.8 = 2.3018 x 10³
Case 2 :
To move the decimal point to the right, we have to count number of digits as explained in the example given below.
According to the example given above, we have to move the decimal point 5 digits to the right and exponent of 10 should be -5 (negative integer)
When we do so, we get the scientific notation of the given number.
Hence, 0.000023 = 2.3 x 10⁻⁵
Important Note:
If we don't find decimal point at anywhere of the given number, we have to assume that there is decimal point at the end of the number.
For example, 2300000 -------------> 2300000.
Here, the non zero digit comes first and decimal point comes next. So we have to apply case 1 to convert this number into scientific notation.
Related topics
- Scientific notations
- Exponents and powers
- Example problems on exponents
- Sample problems on scientific notation
- Negative exponent rules
- Decimals
WORD PROBLEMS
HCF and LCM word problems
Word problems on simple equations
Word problems on linear equations
Word problems on quadratic equations
Area and perimeter word problems
Word problems on direct variation and inverse variation
Word problems on comparing rates
Converting customary units word problems
Converting metric units word problems
Word problems on simple interest
Word problems on compound interest
Word problems on types of angles
Complementary and supplementary angles word problems
Markup and markdown word problems
Word problems on mixed fractrions
One step equation word problems
Linear inequalities word problems
Ratio and proportion word problems
Word problems on sets and venn diagrams
Pythagorean theorem word problems
Percent of a number word problems
Word problems on constant speed
Word problems on average speed
Word problems on sum of the angles of a triangle is 180 degree
OTHER TOPICS
Time, speed and distance shortcuts
Ratio and proportion shortcuts
Domain and range of rational functions
Domain and range of rational functions with holes
Graphing rational functions with holes
Converting repeating decimals in to fractions
Decimal representation of rational numbers
Finding square root using long division
L.C.M method to solve time and work problems
Translating the word problems in to algebraic expressions
Remainder when 2 power 256 is divided by 17
Remainder when 17 power 23 is divided by 16
Sum of all three digit numbers divisible by 6
Sum of all three digit numbers divisible by 7
Sum of all three digit numbers divisible by 8
Sum of all three digit numbers formed using 1, 3, 4
Sum of all three four digit numbers formed with non zero digits
