**Using Scientific Notation :**

Scientific notation is a method of expressing very large and very small numbers as a product of a number greater than or equal to 1 and less than 10, and a power of 10.

A number is written is scientific notation when it is expressed in the form

**a x 10 ^{n }**

where **1 ≤ a < 10 **and **n** may be a positive or negative integer.

To convert the given number into scientific notation, first we have to 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.

Therefore,

2301.8 = 2.3018 x 10^{3}

**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.

Therefore,

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.

The weights of various sea creatures are shown in the table. Write the weight of the Blue whale, Gray whale and Whale shark in scientific notation.

**Weight of Blue whale in scientific notation : **

In the given weight of Blue whale (250,000 lb), we don't find decimal point. So we have to assume that there is decimal point at the end .

Then,

250,000 -----> 250,000.

Number of digits between the first non zero digit and decimal point is 5.

So, the decimal point has to be moved 5 digits to the left and exponent of 10 should be 5 (positive integer)

250,000 = 2.50000 x 10^{5}

250,000 = 2.5 x 10^{5}

(Here, zeros after the decimal point are not taken. Because, they are not valid zeros)

Hence, the weight of Blue whale in scientific notation is

2.5 x 10^{5} lb

**Weight of Gray whale in scientific notation : **

In the given weight of Gray whale (68,000 lb), we don't find decimal point. So we have to assume that there is decimal point at the end .

Then,

68,000 -----> 68,000.

Number of digits between the first non zero digit and decimal point is 4.

So, the decimal point has to be moved 4 digits to the left and exponent of 10 should be 4 (positive integer)

68,000 = 6.8000 x 10^{4}

68,000 = 6.8 x 10^{4}

(Here zeros after the decimal point are not taken. Because, they are not valid zeros)

Hence, the weight of Gray whale in scientific notation is

6.8 x 10^{4} lb

**Weight of Whale shark in scientific notation : **

In the given weight of Whale shark (41,200 lb), we don't find decimal point. So we have to assume that there is decimal point at the end .

Then,

41,200 -----> 41,200.

Number of digits between the first non zero digit and decimal point is 4.

So, the decimal point has to be moved 3 digits to the left and exponent of 10 should be 4 (positive integer)

41,200 = 4.1200 x 10^{4}

41,200 = 4.12 x 10^{4}

(Here, zeros after the decimal point are not taken. Because, they are not valid zeros)

Hence, the weight of Gray whale in scientific notation is

4.12 x 10^{4} lb

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments...

You can also visit our following web pages on different stuff in math.

**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**

**Trigonometry 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**