Question

How do I convert scientific notation to a real number?

Answer 1

Hint:
Given the number in scientific form, \[a \times {10^b}\] where \[1 \leqslant a < 10\]. We have to write the number in standard form. First we will determine the sign of exponent b. Then, move the decimal point to the right or left of a according to the sign of b. If the sign of b is positive then move the decimal b places to the right of a, otherwise move the decimal b places to the left.

Complete step by step solution:
We are given the number in scientific form, \[2.34 \times {10^5}\]
Here, the value of \[b = 5\] which means b is positive, then the decimal moves five places to the right.
To move the decimal to five places first insert 5 zeros at the end of a.
\[ \Rightarrow 2.3400000 \times {10^5}\]
Now, move the decimal to 5 places right.
\[ \Rightarrow 234000.00\]
Therefore, the scientific form of \[2.34 \times {10^5}\] is written as \[234000\]
Also, consider the scientific form, \[2.34 \times {10^{ - 5}}\]
Here, the value of b is negative, which means the decimal moves 5 places to the left by inserting zeros at the beginning of the number.
\[ \Rightarrow 00002.34 \times {10^{ - 5}}\]
Now, move the decimal to 5 places to the left.
\[ \Rightarrow 0.0000234\]

Final answer: Hence, the number from scientific form to real form can be written according to the sign of the exponent.

Note:
The students must remember that the exponent of the scientific number expresses the number of placeholders present, which means the number of places the decimal will move either to the left or right to the value of base. Also, the students please note that if the power of 10 is negative, then it represents the small number in standard form whereas if the power of 10 is positive, it will represent the large number.