Question

How do you subtract $840000000 - 42000000$ and write the answer in scientific notation?

Answer 1

Hint: In scientific notation, a number is written as a product of a number lying between $1$ and $10$, and a power of $10$.
An example of scientific notation is $N \times {10^m}$ where $N$ lies between $1$ and $10$, and involves only significant figures. Scientific notation is used to express too large or too small numbers in the decimal form for a convenient expression. We are given numbers that are written in standard form and we have to convert it into scientific notation and then subtract them.

Complete step-by-step solution:
First, we are finding the scientific notation of $840000000$.
$840000000$ can be written as $84 \times 10000000$
Now, $10000000 = 10 \times 10 \times 10 \times 10 \times 10 \times 10 \times 10$
That is, $84 \times 10000000$ is equal to the product of $84$ and $10$ multiplied with itself $7$ times.
So, it can be written as:
$84 \times 10000000 = 84 \times {10^7} = 840 \times {10^6}$
Hence, the scientific notation of $840000000$ is $840 \times {10^6}$.
Now, we are finding the scientific notation of $42000000$.
$42000000$ can be written as $42 \times 1000000$
Now, $1000000 = 10 \times 10 \times 10 \times 10 \times 10 \times 10$
That is, $42 \times 1000000$ is equal to the product of $42$ and $10$ multiplied with itself $6$ times.
So, it can be written as:
$42 \times 1000000 = 42 \times {10^6}$
Hence, the scientific notation of $42000000$ is $42 \times {10^6}$.
Now, subtract the numbers and take the power of $10$ common.
So, subtracting $42 \times {10^6}$ from $840 \times {10^6}$, we get
$840 \times {10^6} - 42 \times {10^6} = 798 \times {10^6}$
It can be written as: $7.98 \times {10^8}$
Therefore, $840000000 - 42000000 = 7.98 \times {10^8}$.

Note: It can also be solved by using this approach:
To write a number in scientific notation we multiply and divide the given number with the power of $10$ such that the power is equal to (total number of digits$ - 1$), this way the decimal point is placed after the first digit. The scientific notation should contain only significant figures so the digits after the decimal point are rounded off.
Now, the scientific notation can be easily converted into standard form by multiplying the decimal number with the power of $10$. While writing the given number in scientific notation, we see that there is only one significant figure so no decimal will be involved, thus the calculation is easy. This way we can solve similar questions.