# 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, 3^{4 }= 3 × 3 × 3, here the base is 3 and power is 4, so 3 is multiplied by itself 4 times. Another example, 5^{3} = 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,

- 5000 in scientific notation is written as 5 × 10
^{3} - 12500 in scientific notation is written as 1.25 × 10
^{4} - 0.02 in scientific notation is written as 2 × 10
^{-2} - -6700 in scientific notation is written as -6.7 × 10
^{3}

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

Step 15000 ⇢ 5.000Now 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 10^{3}.

Step 25.000 × 10^{3}.

NoteIf the given number is negative just put the negative sign in the result.

Example-5000 —> -5.000 x 10^{3}

Case 2When 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 10.0098 ⇢ 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 29.8 x 10^{-3}This is the scientific notation.

NoteIf 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 × 10

^{5}

**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 × 10

^{3}