Question

How do you write \[{10^{ - 2}}\] in decimal form?

Answer 1

Hint: In the given question, we have been asked to calculate a given expression. To solve the question, we need to know how to convert a negative exponential power to a positive exponential power. We do that, and then we just solve the exponent as normal. We have to express the obtained result as a decimal.

Complete step by step answer:
We have to change \[{10^{ - 2}}\] into decimal.
First, we change the negative exponential power to a positive exponential power.
This is done by taking the reciprocal of the base, hence,
\[{10^{ - 2}} = \dfrac{1}{{{{10}^2}}}\]
Now, we solve the exponent,
\[\dfrac{1}{{{{10}^2}}} = \dfrac{1}{{100}} = 0.01\]

Hence, \[{10^{ - 2}}\] in decimal form is \[0.01\].

Note: For solving the fraction into decimal, we just divide the numerator by the denominator. But, if we have to calculate the reverse – convert a decimal to fraction, we first count the number of digits after the decimal point; let it be ‘c’. Then we take the complete number without the decimal point as the numerator and take the denominator equal to \[1\] followed by \[c\] zeroes.
In this question, we had to convert a number to decimal. We solved it by changing the negative sign in the power to positive - by taking the reciprocal of the given number. Sometimes, some students make the mistake during the conversion; would simply solve the number and forget to bother about the negative sign, which completely changes the answer. So, care must be taken at that point.