What is scientific notation?

Scientific notation is a way of expressing numbers in a more compact and convenient form, especially when working with very large or very small numbers. In scientific notation, a number is represented as the product of a mantissa and a power of 10. A mantissa is a decimal number between 1 and 10, and the power of 10 is used to indicate the scale of the number.
The general form of a number in scientific notation is:
N x 10^n
where N is the mantissa and n is the power of 10. For example, 567,000 can be written as 5.67 x 10^5.
Scientific notation is commonly used in scientific and engineering fields, where very large or very small numbers are often encountered, and it makes mathematical operations involving these numbers much easier.

How do you divide two scientific notation values?

To divide two scientific notation values, you need to follow these steps:
Convert both values to standard notation (i.e. remove the scientific notation):
Step 1:- For example, 5.67 x 10^3 becomes 5670 and 2.34 x 10^2 becomes 234.
Divide the two values:
Step 2:- For example, 5670 ÷ 234 = 24.19
Convert the result back to scientific notation:
Step 3:- To convert 24.19 to scientific notation, we first find the power of 10 that makes the decimal point one place to the right of the first non-zero digit. In this case, it’s 10^1. Then, we multiply the value by 10^1 to obtain the scientific notation form: 2.419 x 10^1.
So, the result of dividing 5.67 x 10^3 by 2.34 x 10^2 is 2.419 x 10^1.

How do you multiply and divide scientific notation?

To multiply and divide scientific notation values, you need to follow these steps:

1. Multiplying:

To multiply two scientific notation values, you first multiply the mantissa (the numbers in front of the x 10^ power) and then add the exponents (the powers of 10).

For example, 2.5 x 10^3 x 4.6 x 10^2 = (2.5 x 4.6) x 10^(3 + 2) = 11.5 x 10^5.

2. Dividing:

To divide two scientific notation values, you first divide the mantissa and then subtract the exponents.
For example, 2.5 x 10^3 ÷ 4.6 x 10^2 = (2.5 ÷ 4.6) x 10^(3 – 2) = 0.54 x 10^1.

Note: When performing these operations, it’s important to ensure that the units of measurement are consistent and match the units being used in the scientific notation expressions.