Question

How do you write $8.9\times {{10}^{3}}$ in standard notation?

Answer 1

Hint: The entire point of expressing in standard notation is representing as whole numbers. The given expression has two different types of terms, one being decimal and the other indices, we convert them to whole numbers one by one. At first, we convert ${{10}^{3}}$ to $1000$ and then $8.9$ to $\dfrac{89}{10}$ and then get the final whole number.

Complete step by step solution:
The given expression that we need to write in standard notation in the problem is $8.9\times {{10}^{3}}$ . By standard form, we mean a whole number without containing any symbols or indices or any other thing. It is a pure whole number. Example of such standard forms is $1256$ .
Now, exponents or indices or powers express repeated multiplication of the same number or term with itself. For example, ${{2}^{3}}$ means the repeated multiplication of $2$ with itself three times. This means ${{2}^{3}}=2\times 2\times 2$ which is nothing but $8$ . In this problem, the term containing indices or exponents or powers is ${{10}^{3}}$ . So, ${{10}^{3}}$ will mean repeated multiplication of $10$ with itself three times. This means ${{10}^{3}}=10\times 10\times 10$ which is nothing but $1000$ .
Decimals are another way to represent fractions, but with base $10$ . For example, $2.985$ means a fraction with numerator as $2985$ and denominator as $1000$ , which is $\dfrac{2985}{1000}$ . Thus, the decimal in the given expression of the problem is $8.9$ which is $\dfrac{89}{10}$ .
The given expression can thus be rewritten as,
$\Rightarrow \dfrac{89}{10}\times 1000$ which after simplification becomes $8900$ .

Therefore, we can conclude that the given expression can be written in standard form as $8900$

Note: There should not be any problem with this method, if we execute it correctly. We can also remember some shortcuts regarding indices and decimals. If we are given some expression as $10$ raised to the power of something, then it means a multiple of $10$ with a number of zeroes equal to the power of $10$ . Also, multiplication of a decimal with some multiple of $10$ means the right shift of the decimal point by the number of digits equal to the number of zeroes in the multiple of $10$ .