Question

What is $4.0$ divided by $0.05$ ?

Answer 1

Hint:We must use scientific notation to solve this problem. We all know that scientific notation is a way of expressing numbers that are either too large or too small to be expressed in decimal form (usually resulting in a long string of digits). It's also known as scientific form, regular index form, or standard form in the United Kingdom.

Complete step by step answer:
Scientists, mathematicians, and engineers often use base ten notation, in part because it simplifies certain arithmetic operations. It's commonly referred to as "SCI" view mode on scientific calculators. Non zero numbers are written in the form in scientific notation.

\[m\times {{10}^{n}}\]. \[m\] times ten raised to the power of \[n\], where n is a positive integer and m is a nonzero real number (usually between 1 and 10 in absolute value, and nearly always written as a terminating decimal). The exponent is the integer n, and the significand or mantissa is the real number $m$.

When it comes to logarithms, the word "mantissa" may be confusing since it is also the standard name for the fractional component of the typical logarithm. In ordinary decimal notation, a minus sign precedes $m$ if the number is negative. The exponent is chosen in normalised notation such that the significand's absolute value (modulus) $m$ is at least 1 but less than 10. So here we have:
\[4=4\times {{10}^{0}}\]
And
\[0.05=5\times {{10}^{-2}}\]
So on dividing we get,
\[\dfrac{4.0}{0.05}=\dfrac{4\times {{10}^{0}}}{5\times {{10}^{-2}}}\]

On simplifying power of 10 we get,
\[\dfrac{4.0}{0.05}=\dfrac{4}{5}\times {{10}^{0+2}}\]
Further we get,
\[\dfrac{4.0}{0.05}=0.80\times {{10}^{2}}\]
We may also write it as
\[\dfrac{4.0}{0.05}=8.0\times {{10}^{-1}}\times {{10}^{2}}\]
Solving power of 10 again we get,
\[\dfrac{4.0}{0.05}=8.0\times {{10}^{-1+2}}\]
And hence we get
\[\therefore\dfrac{4.0}{0.05}=8.0\times {{10}^{1}}\]

Note: One must know that to obtain an accurate and standard result, only the form of significant figures should be used to divide. The general calculation can result in decimal or power of ten miscalculations. Change the numbers with more decimal places to make the questions different.