Chapter 5.5, Problem 3MRE

To determine

To write the given number in scientific notation.

Answer to Problem 3MRE

  $1\times {10}^{-1}$

Explanation of Solution

Given:

Number: $0.1$

Concept used:

Scientific notation is a standard form of writing very large and very small numbers so that it is easy to compare and compute.

The proper format for scientific notation is $a\times {10}^b$ , where $a$ is a number or decimal number such that $1\le \left|a\right|\le 10$ , and $b$ is the power of $10$ required so that the scientific notation is mathematically equivalent to the original number.

Decimal point of a number is moved until the new form is a number from $1$ up to $10$ ( $a$ ), and the exponent is recorded as the number of places decimal point is moved. If the decimal point is moved to the right, then the exponent is negative and if it is moved to the left, the exponent is positive.

Calculation:

To convert $0.1$ to scientific notation,

Move the decimal $1$ place to the right and remove leading zeros to get $1$ .

  $\Rightarrow a=1$

Since the decimal is moved to the right, $b$ is negative

  $\Rightarrow b=-1$

Therefore, the number $0.1$ converted to scientific notation is $1\times {10}^{-1}$ .

Conclusion:

Therefore, scientific notation of $0.1$ is $1\times {10}^{-1}$ .