Write $5.67 \times 10^{-1}$ in standard notation.
A. 0.0567
B. 0.567
C. 56.7
D. 5.67
Answer (2)
We are given the number 5.67 × 1 0 − 1 in scientific notation.
To convert to standard notation, multiply 5.67 by 1 0 − 1 , which is equivalent to dividing by 10.
Calculate 5.67 × 1 0 − 1 = 0.567 .
The number 5.67 × 1 0 − 1 in standard notation is 0.567 .
Explanation
Understanding the Problem We are given the number $5.67
\times 10^{-1}$ in scientific notation. Our goal is to convert this number into standard notation. Scientific notation is a way of expressing numbers that are too big or too small to be conveniently written in standard notation.
Conversion Process To convert a number from scientific notation to standard notation, we need to multiply the decimal part by the power of 10. In this case, we have $5.67
\times 10^{-1}$. This means we need to multiply 5.67 by 1 0 − 1 .
Calculating the Result Recall that 1 0 − 1 is the same as 10 1 or 0.1. So, we need to calculate $5.67
\times 0.1$. This is equivalent to dividing 5.67 by 10.
Final Calculation When we multiply 5.67 by 0.1 (or divide by 10), we move the decimal point one place to the left: $5.67
\times 0.1 = 0.567$.
Conclusion Therefore, $5.67
\times 10^{-1}$ in standard notation is 0.567. Looking at the multiple-choice options, we see that option B is the correct answer.
Examples
Scientific notation and standard notation are useful in many real-world scenarios. For example, scientists use scientific notation to express very large or very small numbers, such as the distance to stars or the size of atoms. Converting between scientific and standard notation helps us understand the magnitude of these numbers in a more intuitive way. Imagine you're working with measurements in a lab, and you need to convert a value from scientific notation (like $3.2
\times 10^{-6}$ meters) to standard notation (0.0000032 meters) to properly set up your equipment. This conversion ensures accuracy and helps you visualize the scale of the measurement.
The number 5.67 × 1 0 − 1 in standard notation is 0.567. This is obtained by multiplying 5.67 by 1 0 − 1 , which is equivalent to dividing by 10. Therefore, the correct answer is option B.
;
