SCIENTIFIC NOTATION RULES

Here we are going to see, "Scientific notation rules"

Scientific notation rules

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

a x 10n     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.

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

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.

Practice questions

To have better understanding, let us go through some practice questions on "Scientific notation rules".

Question 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".

Question 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 decimal point  =  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 10⁶  = 5.4 x 10

Hence, 5400000 = 5.4 x 10

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

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

Question 3 :

Write the given number in scientific notation.

71 x 10²

Solution :

Here we don't find decimal point in 71x 10². So we have to assume that there is decimal point at the end of 71

Then, 71x 10² ---------> 71x 10²

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 decimal point  =  1

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

71x 10² = 7.1 x 10¹ x 10²

71x 10² = 7.1 x 10³

Hence, 71 x 10² = 7.1 x 10³

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

Question 4 :

Write the given number in scientific notation.

33 x 10³

Solution :

Here we don't find decimal point in 33 x 10³ So we have to assume that there is decimal point at the end of  33

Then, 33x 10³ ---------> 3310³

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 decimal point  =  1

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

3310³  = 3.3 x 10¹ x 10³

3310³  = 3.3 x 10²

Hence, 33x 10³   =  3.3 x 10²

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

Question 5 :

Write the given number in scientific notation.

0.63 x 10³

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 = 1

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

0.63 10³  = 6.3 x 10¹ x 10³

0.63 10³  = 6.3 x 10

Hence, 0.63 10³  = 6.3 x 10⁴

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

Question 6 :

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

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

Question 7 :

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

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

Question 8 :

Write the given number in scientific notation.

804 x 10²

Solution :

Here we don't find decimal point in 804 x 10² . So we have to assume that there is decimal point at the end .

Then, 804 x 10² ---------> 804. x 10²

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 decimal point  =  2

So, the decimal point has to be moved 2 digits to the left and exponent of 10 should be 2 (positive integer)

804. x 10² =  8.04 x 10² x 10²

804. x 10² =  8.04 x 10

Hence,  804 x 10² =  8.04 x 10

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

Question 9 :

Write the given number in scientific notation.

4.8

Solution :

Here the given number is almost in scientific notation.

Because there is only one non zero digit before the decimal point.

We don't have to move the decimal point either to the left or right.

Then, exponent of 10 should be zero.

4.8 = 4.8 x 10

Hence,  4.8 = 4.8 x 10

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

Question 10 :

Write the given number in scientific notation.

0.99 x 10¹

Solution :

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

We have to move the decimal to the right.

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

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

0.99 10¹  = 9.9 x 10¹ x 10¹

0.99 10¹  = 9.9 x 10

Hence, 0.99 10¹  = 9.9 x 10

After having gone through the stuff and examples, we hope that the students would have understood "Scientific notation rules".

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