Question

Express the following numbers in scientific notation:
(i) 0.0048
(ii) 234,000
(iii) 8008
(iv) 500.0
(v) 6.0012

Answer 1

Hint: Scientific notation is a way of representing very large or very small numbers that are written in decimal form to a simpler form i.e. a number that is written in scientific notation when a number between 1 and 10 is multiplied by a power of 10. Numbers written in scientific notation are written in the form\[A \times {10^n}\] , where A is a number between 1 and 10, but not 10 itself, and n is any integer (positive or negative number).

Complete Step by Step Solution:
Steps to write a number in scientific notation are as follows:-
For a large number,
Step 1: Move the decimal point to the left to create a number greater than or equal to 1 and less than 10.
Step 2: Calculate the number of decimal places you moved the decimal point to the left and use that number as the positive power of 10.
Step 3: Substitute the value of A and n in the general form of scientific notation i.e.
For a small number,
Step 1: Move the decimal point to the left to create a number greater than or equal to 1 and less than 10.
Step 2: Calculate the number of decimal places you moved the decimal point to the right and use that number as the negative power of 10.
Step 3: Substitute the value of A and n in the general form of scientific notation i.e.

Hence, of the given options:
(1) 0.0048 in scientific notation is \[4.8 \times {10^{ - 3}}\] .
(2) 234,000 in scientific notation is \[2.34 \times {10^5}\] .
(3) 8008 in scientific notation is \[8.008 \times {10^3}\] .
(4) 500.0 in scientific notation is \[5.000 \times {10^2}\] .
(5) 6.0012 in scientific notation is 6.0012.

Note: To determine the power or exponent of 10, we must follow the rules listed below:
1) The base should always be 10.
2) The exponent must be a non-zero integer (it can be either positive or negative).
3) The absolute value of the coefficient is greater than or equal to 1 but it should always be less than 10.
4) Coefficient can be a positive or negative number including whole and decimal numbers.