CONVERT BETWEEN STANDARD AND SCIENTIFIC NOTATION

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. 

Standard Form to Scientific Notation 

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

a x 10ⁿ

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

To convert a number to 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 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. 

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.  

Scientific Notation to Standard Form

To convert a number from scientific notation to standard notation, first we have to notice the exponent of 10 in scientific notation.

If the exponent of 10 is positive, we have to move the decimal point to the right. 

For example, if you have 10³, you have to move the decimal point 3 digits to the right. 

If the exponent of 10 is negative, we have to move the decimal point to the right. 

For example, if you have 10^-5, you have to move the decimal point 5 digits to the left. 

Example 1 :

Write the following number in standard form.  

5.236 x 10⁵

Solution :

Here, the exponent of 10 is positive 5. So we have to move the decimal point five digits to the right.

In 5.236, we have only three digits after the decimal point.

So, we have to add two zeros to move the decimal point five digits to the right.   

Therefore, the standard form of 5.236 x 10⁵ is 

523600

Example 2 :

Write the following numbers in standard form.

6.415 x 10^-6

Solution :

Here, the exponent of 10 is negative 6. So we have to move the decimal point six digits to the left.

In 6.415, we have only 1 digit before the decimal point.

So, we have to add five zeros to move the decimal point six digits to the left.   

Therefore, the standard form of 6.415 x 10^-6 is 

0.000006415

To get practice problems on standard form  and scientific notation,

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