How to write numbers in scientific notation?

Exponent is a mathematical operation, it represents how many times a number is multiplied by itself. It involves two numbers called base and power, power is written as a superscript of the base. it shows base is multiplied by itself power number of times. See example, 3⁴ = 3 × 3 × 3, here the base is 3 and power is 4, so 3 is multiplied by itself 4 times. Another example, 5³ = 5 × 5 × 5, here the base is 5 and power is 3, so 5 is multiplied by itself 3 times.

Scientific notation

Scientific notation is useful for representing a very large or very small number skillfully. It is used for numbers in order to write numbers in standard form, also it helps in writing large numbers. In Scientific notation, a number is written as,

a × 10^b

• Where a is a non-zero number lie between 1 to 10 i.e. 1 ≤ a < 10 and be negative also and b can be any number.
• Here b+1 shows the number of digits in the given number.

For example,

1. 5000 in scientific notation is written as 5 × 10³
2. 12500 in scientific notation is written as 1.25 × 10⁴
3. 0.02 in scientific notation is written as 2 × 10^-2
4. -6700 in scientific notation is written as -6.7 × 10³

How to write numbers in scientific notation?

Answer:

In order to express numbers in scientific notation, lets take a look at the below-given cases,

Case 1 When a positive number is greater than 1mIn such a case put a decimal after the first digit.

Step 1 5000 ⇢ 5.000

Now to balance it multiply it by 10^{(b – 1)} where b is the number of digits in the given number, here the number consists of 4 digits so multiply it by 10³.

Step 2 5.000 × 10³.

Note If the given number is negative just put the negative sign in the result.

Example -5000   —>   -5.000 x 10³

Case 2 When the positive number is a very small number i.e. smaller than 1 but greater than 0.

In such a case multiply the number by 10 until it is less than 1, and count how many times you multiply it.

Step 1 0.0098 ⇢ 9.8 (multiplied number 3 times)

Now the number is multiplied by 10 m times. you have to divide the number by 10 m times, to balance it. So instead of dividing it by 10^m multiply it by 10^-m because both means the same.

Step 2 9.8 x 10^-3 

This is the scientific notation.

Note If the given number is negative just put the negative sign in the result.

Sample Problem

Question1: Convert 70000 into scientific notation.

Solution:

Number of digits is 5

So, 70000 = 7 × 10^-5

Question2: Convert -0.0000845 into scientific notation

Solution: 

There are 5 digits to reach the first non zero digit

So, -0.0000845 = -8.45 × 10⁵

Question3: Convert 7346.0431 into scientific notation.

Solution:

There are 3 digits for decimal point to reach the first digit

So, 7346.0431 = 7.3460431 × 10³