Question

How do you write \[1.2 \times {10^4}\] in standard notation?

Answer 1

Hint: We know that the number of places the decimal point moves is the power of the exponent, because it represents a power of 10. The number of places the decimal point moves is the power of the exponent, because it represents a "power of 10". A positive number is written in scientific notation if it is written as \[a \times {10^n}\] where the coefficient a has a value such that \[1 \leqslant a \leqslant 10\] and n is an integer, hence based on the given exponent we need to write the standard notation.

Complete step by step solution:
Given,
 \[1.2 \times {10^4}\] , in which we need to write the given number in standard notation.
The rule to write a number in standard notation is that the number of places the decimal point moves is the power of the exponent, because it represents a power of 10.
The exponent of 10 is the number of places the decimal point must be shifted to give the number in long form. A positive exponent shows that the decimal point is shifted that number of places to the right. A negative exponent shows that the decimal point is shifted that number of places to the left.
Here, the exponent in the 10’s term is positive, hence move the decimal point four places to the right as:
 \[1.2 \times {10^4} = 12,000\] .
So, the correct answer is “12,000”.

Note: The key point to write the given number in standard notation is that, we need to see the exponent of the given number such that based on the exponent we need to shift the decimal places of the given number as it represents a "power of 10". To multiply numbers in scientific notation, first multiply the numbers that aren’t powers of 10 (the a in \[a \times {10^n}\] ). Then multiply the powers of ten by adding the exponents. This will produce a new number times a different power of 10.