Scientific notation is a standard way of writing very large and very small numbers so that they’re easier to both compare and use in computations.

Every number in the scientific notation must be in the form of

**a x 10 ^{n}**

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

To convert a 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.

So,

**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.

So,

**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.

**Problem 1 :**

Write the given number in scientific notation.

0.00006

**Solution :**

Here decimal point comes first at non zero digit comes next.

We have to move the decimal point to the right.

No. of digits from the decimal point up to the first non zero digit is 5.

So, the decimal point has to be moved 5 digits to the right and exponent of 10 should be -5 (negative integer)

So, the scientific notation of 0.00006 is

6 x 10^{-5}

**Problem 2 :**

Write the given number in scientific notation.

5400000

**Solution :**

Here we don't find decimal point in 5400000. So we have to assume that there is decimal point at the end .

Then, 5400000 ---------> 5400000.

Here non zero digit comes first and decimal point comes next.

We have to move the decimal point to the left.

No. of digits between the 1st non zero digit and the decimal point is 6.

So, the decimal point has to be moved 6 digits to the left and exponent of 10 should be 6 (positive integer)

5400000 = 5.400000 x 10^{6}

5400000 = 5.4 x 10^{6}

So, the scientific notation of 5400000 is

5.4 x 10^{6}

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

**Problem 3 :**

Write the given number in scientific notation.

71 x 10^{2}

**Solution :**

Here we don't find decimal point in 71x 10^{2}. So we have to assume that there is decimal point at the end of 71

Then,

71 x 10^{2} ---------> 71. x 10^{2}

Here non zero digit comes first and decimal point comes next.

We have to move the decimal point to the left.

No. of digits between the 1st non zero digit and the decimal point is 1.

So, the decimal point has to be moved 1 digit to the left and exponent of 10 should be 1 (positive integer)

71. x 10^{2} = 7.1 x 10^{1} x 10^{2}

71

So, the scientific notation of 71 x 10^{2} is

7.1 x 10^{3}

**Problem 4 :**

Write the given number in scientific notation.

33 x 10^{-3}

**Solution :**

Here we don't find decimal point in 33 x 10^{-3} So we have to assume that there is decimal point at the end of 33

Then,

33 x 10^{-3} ---------> 33. x 10^{-3 }

Here non zero digit comes first and decimal point comes next.

We have to move the decimal point to the left.

No. of digits between the 1st non zero digit and the decimal point is 1.

So, the decimal point has to be moved 1 digit to the left and exponent of 10 should be 1 (positive integer)

33. x 10^{-3} = 3.3 x 10^{1} x 10^{-3}

33. x 10^{-3} = 3.3 x 10^{-2}

So, the scientific notation of 33 x 10^{-3} is

3.3 x 10^{-2}

**Problem 5 :**

Write the given number in scientific notation.

0.63 x 10^{-3}

**Solution : **

Here decimal point comes first and non zero digit comes next.

We have to move the decimal point to the right.

No. of digits from the decimal point up to the first non zero digit is 1.

So, the decimal point has to be moved 1 digit to the right and exponent of 10 should be -1 (negative integer)

0.63 x 10^{-3} = 6.3 x 10^{-1} x 10^{-3}

0.63 x 10^{-3} = 6.3 x 10^{-4}

So, the scientific notation of 0.63 x 10^{-3} is

6.3 x 10^{-4}

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

If you have any feedback about our math content, please mail us :

**v4formath@gmail.com**

We always appreciate your feedback.

You can also visit the 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**