Question

Convert the following numbers in the decimal form.
i) \[3.25 \times {10^{ - 6}}\]
ii) $4.134 \times {10^{ - 4}}$
iii) $4.134 \times {10^4}$
iv) $1.86 \times {10^7}$
v) $9.87 \times {10^9}$
vi) $1.432 \times {10^{ - 9}}$

Answer 1

Hint: We are given with the numbers written in scientific notation in the question. To convert the scientific notation in the decimal, move the decimal to the left side depending on the exponent on the \[10\], if the exponent of \[10\]is negative and if exponent in \[10\]is positive then move the decimal places to the right side.

Complete Step by Step Solution:
We know that, the scientific notation is of the form –
$m \times {10^n}$
where, $n$ is the power.
Therefore, we can conclude that the numbers given in the question are in scientific notation. So, we have to convert them into decimal form.
To convert the scientific notation into decimal form, if the exponent in the \[10\]is negative we move the decimal to the left side in the number to the $n$ places, where, $n$ is the exponent of \[10\], while, if the exponent is positive then, we move the decimal point to the right side of the number depending on the to the $n$ places.
Using the above statement, now, converting \[3.25 \times {10^{ - 6}}\] , $4.134 \times {10^{ - 4}}$, $4.134 \times {10^4}$ , $1.86 \times {10^7}$, $9.87 \times {10^9}$ , $1.432 \times {10^{ - 9}}$ -
i) In \[3.25 \times {10^{ - 6}}\] , the power is $6$ and negative, so, moving decimal point $6$places to the left side, we get, $0.00000325$
ii) In $4.134 \times {10^{ - 4}}$ , again the power is $4$ and negative, so, moving decimal point $4$places to the left side, we get, $0.0004134$
iii) In $4.134 \times {10^4}$ , the power is $4$and positive, so, moving decimal point $4$places to the right side, we get, $41340$
iv) In $1.86 \times {10^7}$ , the power is $7$ and positive, so, moving decimal point $7$places to the right side, we get, $18600000$
v) In $9.87 \times {10^9}$ , the power is $9$ and positive, so, moving decimal point $9$places to the right side, we get, $9870000000$
vi) In $1.432 \times {10^{ - 9}}$ the power is $9$and negative, so, moving decimal point $9$places to the left side, we get, $0.000000001432$
Hence, we converted the scientific notation into decimal form.

Note:
We can also convert the scientific notation into decimal form by dividing, we know that, if any number has negative power then, we can write it as, $\dfrac{1}{{{m^n}}}$ where, $m$ is the number having negative exponent, $n$. So, let if we have to convert, \[3.25 \times {10^{ - 6}}\] then, to convert it into decimal form we can write it as –
$ \Rightarrow \dfrac{{3.25}}{{{{10}^6}}}$
Then, calculate ${10^6}$ and divide $3.25$ and we will get our answer.