# Operations on Scientific Notations worksheet

## Addition and subtraction in scientific notation:

While performing basic arithmetic operations like addition, subtraction, multiplication or division on numbers written in scientific notation, we need to be careful and should follow some rules to reach the correct answer.

While adding and subtracting the numbers in scientific notation, exponent part of all the numbers must be same. If it is not same , then first make it same and then combine the numbers.

**Don’t forget to write the final answer in scientific notation.**

### When exponent part is same-

Example1: Combine and

Solution: Here we see that exponent part of both numbers is same (). So we just need to combine the coefficients of these two numbers.

+ =

=

As the coefficient part can’t exceed 10, so we need to convert this result into scientific notation.

=

### When exponent part is not same-

Example2: Simplify the following expression:

Solution: As the exponent part is not same, we make them same first.

Again you can do it two ways. Either lower the exponent to or you can raise the exponent to

**First way: raise the exponent to **

As we know, when decimal is moved to left, exponent is positive (increased). We need to raise the exponent by 2 so decimal is moved towards left by 2 places and we get

=

=

=

=

**Second way: Either lower the exponent to **

When decimal is moved to right, exponent is negative (decreased). We need to lower the exponent by 2 so decimal is moved towards right by 2 places and we get

=

=

But this result is not in scientific notation. To get it in scientific notation decimal should be placed after first significant digit.

So final answer is

Example3. Simplify the expression

Solution: =

=

=

=

Then we convert it into scientific notation and get answer as

Example4. Simplify the expression

Solution: =

=

=

=

Rewriting it as scientific notation we get the final answer as

**Practice problems:**

Simplify each problem and write the answer in scientific notation.

Answers:

1)

2)

3)

4)