Question

How do you write $0.0025 \times 111.09$ in scientific notation?

Answer 1

Hint: In order to express the numbers in scientific notation form, we simply multiply or divide each number with $10$ and its consequent powers in such a way so that we only have one number before the decimal point. If we are multiplying, then the powers on base $10$ are in positive form, while if we are dividing then the powers are in negative form.

Complete step-by-step solution:
In the given question, we have been asked to write the numbers $0.0025 \times 111.09$ in scientific notation. We use scientific notation when we wish to express a number which is either very small or very large. Now, any number containing decimal points can be expressed in scientific notation. To express a number in scientific notation, we simply need to multiply the respective number with ten raised to a particular power depending on the number.
$0.0025$ can be expressed in scientific notation as: $2.5 \times {10^{ - 3}}$ . Here, we use a negative power on $10$ because we need to divide the respective number with $1000$ to get our original number of $0.0025$ .
$111.09$ can be expressed in scientific notation as: $1.1109 \times {10^2}$ . Here we use a positive power on base $10$ as we need to multiply the respective number with $100$ to get that number in its original form.
Thus, together the numbers are: $2.5 \times {10^{ - 3}} \times 1.1109 \times {10^2}$
Further, we know that ${a^m} \times {a^n} = {a^{m + n}}$ .Using this, we get the above equation as –
$2.5 \times 1.1109 \times {10^{2 - 3}} = 2.5 \times 1.1109 \times {10^{ - 1}}$

Hence, $0.0025 \times 111.09$ in scientific notation can be expressed as $2.5 \times 1.1109 \times {10^{ - 1}}$ .

Note: Scientific notation is a way of expressing numbers which are very large or very small. Numbers in scientific notation are made of three parts: coefficient, base and exponent. To express any number in this form, we simply multiply it with $10$ raised to a particular power. When a number is $10$ or greater, the decimal point has to move to the left, and the power of $10$ is positive, while if the number is smaller than $1$, and the decimal point moves to the right, the power of $10$ is negative.