Convert to Scientific Notation

A scientific notation is based on our number system in which the places are defined in accordance with powers of 10.

A scientific notation is used to represent numbers that are very large or very small. This notation was framed by the scientists and mathematicians as a convenient tool of expression. It is also very easy to do the algebraic operations and simplify the calculations with large numbers or small numbers or especially while dealing both simultaneously.

Let us see how it operates on practical fields.

convert to scientific notation – Form of notation

A scientific notation is denoted in the following form

a x 10n, where,  1= I a I < 10

That is always express the number within 1 to 10 times to the power 10. It is very obvious that if ‘n’ is positive, the number will be large and if negative, the number will be small.

convert to scientific notation – Practical examples

Let us take a few examples of numbers to convert into scientific notation.

The average distance to the Moon from our Earth is about 384,000 kilometers.

Instead of writing in this form, it can conveniently be expressed in scientific notation. To convert to scientific notation, consider the prominent digits 3, 8 and 4. These digits could be rewritten as 3.84 as per the norms stipulated for scientific notation. If you place a decimal point between 3 and 8 in the given number, then there are five places after the decimal point.

3.84000

Since each place is worth a10, 3.84 has to be multiplied by 105. Therefore, in scientific notation

384,000 kilometers = 3.84 x 105 km.

The diameter of a carbon atom is about  0.000000022 cm. Let us covert to scientific notation. The compatible number for the scientific notation is 2.2. In such a case let us count the number of places the decimal point in the given number to be shifted.

0.000000022

It is 8.

Since we are shifting the decimal point to the right, each place is reduced by a 10. Therefore,

0.000000022 cm = 2.2 x 10-8

Example problems based on scientific terms and concepts:

The example problems based on scientific terms and concepts is given below that,

Example 1:

How do you convert 75000 in scientific notation?

Solution:

Step 1:

The given number is 75000.

Step 2:

The given number is not a big number, but it is simple to convert scientific notation.

First rounding 7.5 x 104 = 75000 [104 = 10000]

Step 3:

The concluding answer for scientific terms and concepts are 7.5 x 104.

Example 2:

How do you convert 4510000 in scientific notation?

Solution:

Step 1:

The given number is 4510000.

Step 2:

The given number is a big number, but it is simple to convert scientific notation.

First rounding 4.51 this is not equivalent to the given number.

Step 3:

Here, 6 digits subsequent the decimal point.

So, 4.51 × (1000000)

Therefore the rounding will be 106.

Step 4:

The concluding answer for scientific terms and concepts are 4.51 x 106

Practice problems based on scientific terms and concepts:

Problem 1:

How do you convert 7610000 in scientific notation?

Answer: The concluding answer for scientific terms and concepts are 7.61 x 106.

Problem 2:

How do you convert 590000 in scientific notation?

Answer: The concluding answer for scientific terms and concepts are 5.9 x 105.