Question

How do you express \[3.347\times {{10}^{-1}}\] in standard form?

Answer 1

Hint: In this problem, we have to express \[3.347\times {{10}^{-1}}\] in standard form. To convert a number to standard form, place the decimal to the right of the first non-zero digit. So now we have to convert the exponent to its fraction, then we can convert the fraction part to the decimal point, that is 10 to the power -1 should be converted to the decimal point. Now we multiplied it with the rest of the number to get the standard form of the given number \[3.347\times {{10}^{-1}}\] .

Complete step by step answer:
We know that the given number to express in standard form is \[3.347\times {{10}^{-1}}\].
We can convert the exponent form to its fraction, that is \[{{10}^{-1}}\] in fraction form.
\[\Rightarrow {{10}^{-1}}=\dfrac{1}{10}\]
Now we can convert it to the decimal form, we get
\[\Rightarrow \dfrac{1}{10}=0.1\]
Now we can multiply this 0.1 in the given expression instead of \[{{10}^{-1}}\], we get
\[\Rightarrow 3.347\times 0.1\]
Here, we can move the decimal point one place to the left to get the standard form, we get
\[\Rightarrow 0.3347\]
Therefore, the standard form of \[3.347\times {{10}^{-1}}\] is 0.3347.

Note:
Students make mistakes in converting the exponent part to the decimal form. We should know that to solve these types of problems, we have to know how to move the decimal points to the left and right respectively of the given problem. We have to move left when we have a negative exponent and move right when we have a positive exponent.