Question

Write the following in standard form 0.00000564.

Answer 1

Hint: In this type of questions, we have to make the given digit as in the form, standard form = $N \times {10^n}$where $1 \leqslant N < 10$
Here we have 0.00000564,

Complete step-by-step solution:
To convert this digit in standard form, we will divide and multiply this by ${10^x}$such that x is number of 0’s in the given digit.
\[ \Rightarrow 0.00000564 = \dfrac{{{{10}^5}}}{{{{10}^5}}} \times 0.00000564\]
\[ \Rightarrow 0.00000564 = 0.564 \times {10^{ - 5}}\] ………………… (i)
Here 0.564 is not $ \geqslant $ and we want it as $1 \leqslant N$ so we will divide it in such way that we will get the value of $1 \leqslant N$
Now we will divide and multiply 0.564 by 10,
\[ \Rightarrow 0.564 = \dfrac{{10}}{{10}} \times 0.564\]
\[ \Rightarrow 0.564 = 5.64 \times {10^{ - 1}}\] …………………….. (ii)
Now put value of equation (ii) in equation (i), we get
\[ \Rightarrow 0.00000564 = 5.64 \times {10^{ - 1}} \times {10^{ - 5}}\]
Now, simplifying this, we will get
\[ \Rightarrow 0.00000564 = 5.64 \times {10^{ - 6}}\]
Here N = 5.64, such that $1 \leqslant N < 10$
Hence the standard form of 0.00000564 is \[5.64 \times {10^{ - 6}}\]

Note: In these types of questions we have to make the given number in the standard form by reducing the number of digits after decimal. We have to make sure that the number of digits after the decimal must be as less as possible by multiplying the number with 10 raised to power n and n can be any integer value.