Question

Express the number \[4\cdot 5\times {{10}^{4}}\] in simplest form.

Answer 1

Hint: As we know a number expressed in the form of \[k\times {{10}^{n}},\] where k is a terminating decimal such that \[1\le k<10\]and\[n\] is any Integer, is said to be in scientific notation or standard form of notation. In standard exponential notation, the number is always written with only one digit to the left of the decimal. If the decimal point moves to the left or the number is large, add the number of places the decimal moves to the current exponent of ten.

Complete step by step solution:
\[4\cdot 5\times {{10}^{4}}\]
By expanding the power of\[10,\]we get
\[4\cdot 5\times 10000\]
By multiplication, we get
\[45000\]

Note: If the decimal point moves to the right or the number is small, subtract the number of places the decimal moves from the current exponent of ten.