Question

Express the following number in standard form: 600,000,000

Answer 1

Hint: We calculate the number of 0 digits in the given number and write them as a product of number 10 with each other. Use the rule of exponents to collect power of the terms having the same base i.e. to collect the powers of 10.
* If we have m and n as two numbers, then \[{m^p}.{m^q} = {m^{p + q}}\]
* Standard form of a number is that form where we can write any number as a decimal number between 1.0 and 10.0 multiplied by the powers of 10. Example: \[5.7 \times {10^9}\]

Complete step-by-step solution:
We have to find the standard form of the number 600,000,000
We first calculate the number of zeroes in the given number.
Here 600,000,000 has 8 zeros i.e. 10 is multiplied 8 times.
So, we can write \[600,000,000 = 6 \times 100000000\]...............… (1)
Now we can separate the number 100000000 as multiples of 10
i.e. we can write \[100000000 = 10 \times 10 \times 10 \times 10 \times 10 \times 10 \times 10 \times 10\].................… (2)
Substitute the value from equation (2) in equation (1)
\[ \Rightarrow 600,000,000 = 6 \times 10 \times 10 \times 10 \times 10 \times 10 \times 10 \times 10 \times 10\]
Now we know we can collect the powers of numbers having the same base. Here we collect the powers of number 10.
\[ \Rightarrow 600,000,000 = 6 \times {10^{1 + 1 + 1 + 1 + 1 + 1 + 1 + 1}}\]
\[ \Rightarrow 600,000,000 = 6 \times {10^8}\]
Since the first digit is a decimal number between 1.0 and 10.0 i.e. 6.0 and is multiplied with powers of 10 then it is a standard form.

\[\therefore \]Standard form of 600,000,000 is \[6 \times {10^8}\].

Note: Many students think 6 is not a decimal number so to convert it into a decimal number they divide both the terms by 10 which gives us answer \[0.6 \times {10^7}\] which is wrong as the first number should be the number between 1 and 10 and 0.6 is less than 1.