# SCIENTIFIC NOTATION WITH NEGATIVE POWERS OF 10

## About "Scientific notation with negative powers of 10"

Scientific notation with negative powers of 10 :

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

## Scientific notation with negative powers of 10 - Rules

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

a x 10

where 1 ≤ a < 10 and n is a a negative integer.

To convert the given number into scientific notation, first we have to identify where the decimal point and non zero digit come.

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

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 with negative powers of 10 - Examples

Example 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 decimal point up to the first non zero digit = 5

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

Hence, 0.00006 = 6 x 10

Let us look at  the next problem on "Scientific notation rules".

Example 2 :

Write the given number in scientific notation.

0.000216

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 decimal point up to the first non zero digit = 4

So, the decimal point has to be moved 4 digits to the right and exponent of 10 should be -4 (negative integer)

0.000216   =  2.16 10

Hence, 0.000216  =  2.16 10

Example 3 :

Write the given number in scientific notation.

0.0000009

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 decimal point up to the first non zero digit = 7

So, the decimal point has to be moved 7 digits to the right and exponent of 10 should be -7 (negative integer)

0.0000009   =  9 10

Hence, 0.0000009   =  9 10

After having gone through the stuff given above, we hope that the students would have understood "Scientific notation with negative powers of 10"

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