Question

How do you write $0.143$ in scientific notation ?

Answer 1

Hint: In this question, we need to write the given number in scientific notation. Scientific notation is a way of writing very large or very small numbers. A number is written in scientific notation when a number between 1 and 10 multiplied by a power of 10. In the given question firstly, we will move the decimal place to the right to create a new number from 1 up to 10. Then we determine the exponent and at last we will write it in a standard form, which will be of the form ${\text{N}} \times {10^m}$.

Complete step-by-step solution:
Given a number of the form $0.143$
We are asked to write it in scientific notation.
Firstly, let us understand the meaning of scientific notation.
Scientific notation is a method of expressing numbers in terms of a decimal number between 1 and 10, but not 10 itself multiplied by a power of 10.
All numbers in scientific notation or standard form are written in the form ${\text{N}} \times {10^m}$,
where ${\text{N}}$ is a number between 1 and 10, but not 10 itself and $m$ is any integer (positive or negative number).
The real number ${\text{N}}$ is called the significand and $m$ is called the order of magnitude.
Now we convert $0.143$ into scientific notation as follows.
In the first step, move the decimal one times to right in the number, so that the resulting number is greater than or equal to 1 but less than 10.
So we get, ${\text{N = 1}}{\text{.43}}$
In the second step, we will determine the exponent, it will be the number of times we moved the decimal right or left.
Here we moved the decimal to the right, so the exponent $m$ is negative.
Hence we get, $m = - 1$.
In the third step, we write the number in the scientific notation form ${\text{N}} \times {10^m}$.
Hence we get, $1.43 \times {10^{ - 1}}$.
Therefore, the scientific notation form of $0.143$ is given by $1.43 \times {10^{ - 1}}$.

Note: We must remember that a positive exponent shows that the decimal point is shifted to the right of that number and a negative exponent shows that the decimal point is shifted to the left of that number. The digit term in the scientific notation indicates the number of significant figures in the number. The exponential term only places the decimal point.
While writing the numbers in the scientific notation, we have to follow certain rules as follows.
(1) The scientific notations are written in two parts, one is just the digit with the decimal point placed after the first digit, followed by multiplication with 10 to a power number of decimal point, that puts the decimal point where it should be.
(2) If the given number is greater than 1 and multiples of 10, then the decimal point has to move to the left, and power of 10 will be positive.
(3) If the given number is smaller than 1, then the decimal point has to move to the right, and the power of 10 will be negative.