(a) A Certain Solution Has A Hydrogen Ion Concentration Of $8.96 \times 10^{-4}$ Moles Per Liter. Write This Number In Standard Notation.(b) A Black Rhinoceros Can Weigh Up To 6400 Pounds. Write This Number In Scientific Notation.(a)
Introduction
In chemistry, it is essential to express numbers in a clear and concise manner. Standard notation and scientific notation are two ways to represent large or small numbers. In this article, we will discuss how to convert numbers from one notation to another.
Converting Scientific Notation to Standard Notation
(a) Converting to Standard Notation
To convert a number from scientific notation to standard notation, we need to move the decimal point to the left by the number of places indicated by the exponent. In this case, the exponent is -4, which means we need to move the decimal point 4 places to the left.
Step 1: Move the decimal point 4 places to the left
8.96 × 10^(-4) = 0.000896
Step 2: Write the number in standard notation
The number in standard notation is 0.000896.
(b) Converting 6400 to Scientific Notation
To convert a number from standard notation to scientific notation, we need to move the decimal point to the right until we have a number between 1 and 10. Then, we multiply the number by 10 raised to the power of the number of places we moved the decimal point.
Step 1: Move the decimal point to the right until we have a number between 1 and 10
6400 → 6.4 (moved the decimal point 3 places to the right)
Step 2: Write the number in scientific notation
The number 6400 in scientific notation is 6.4 × 10^3.
Discussion
In chemistry, it is essential to express numbers in a clear and concise manner. Standard notation and scientific notation are two ways to represent large or small numbers. By converting numbers from one notation to another, we can make calculations and comparisons easier.
Examples of Converting Numbers to Scientific Notation
(a) Converting 0.000456 to Scientific Notation
To convert a number from standard notation to scientific notation, we need to move the decimal point to the right until we have a number between 1 and 10. Then, we multiply the number by 10 raised to the power of the number of places we moved the decimal point.
Step 1: Move the decimal point to the right until we have a number between 1 and 10
0.000456 → 4.56 (moved the decimal point 4 places to the right)
Step 2: Write the number in scientific notation
The number 0.000456 in scientific notation is 4.56 × 10^(-4).
(b) Converting 0.0000009 to Scientific Notation
To convert a number from standard notation to scientific notation, we need to move the decimal point to the right until we have a number between 1 and 10. Then, we multiply the number by 10 raised to the power of the number of places we moved the decimal point.
Step 1: Move the decimal point to the right until we have a number between 1 and 10
0.0000009 → 9 × 10^(-7) (moved the decimal point 7 places to the right)
Step 2: Write the number in scientific notation
The number 0.0000009 in scientific notation is 9 × 10^(-7).
Conclusion
Introduction
In our previous article, we discussed how to convert numbers from standard notation to scientific notation and vice versa. In this article, we will answer some frequently asked questions about converting numbers to standard and scientific notation.
Q&A
Q: What is the difference between standard notation and scientific notation?
A: Standard notation is a way of writing numbers in a straightforward manner, without any exponents. Scientific notation, on the other hand, is a way of writing numbers in a compact form, using exponents to represent large or small numbers.
Q: How do I convert a number from standard notation to scientific notation?
A: To convert a number from standard notation to scientific notation, you need to move the decimal point to the right until you have a number between 1 and 10. Then, you multiply the number by 10 raised to the power of the number of places you moved the decimal point.
Q: How do I convert a number from scientific notation to standard notation?
A: To convert a number from scientific notation to standard notation, you need to move the decimal point to the left by the number of places indicated by the exponent. In this case, the exponent is -4, which means you need to move the decimal point 4 places to the left.
Q: What is the exponent in scientific notation?
A: The exponent in scientific notation is a small number that tells you how many places to move the decimal point. If the exponent is positive, you move the decimal point to the right. If the exponent is negative, you move the decimal point to the left.
Q: Can I have a negative exponent in scientific notation?
A: Yes, you can have a negative exponent in scientific notation. In this case, you move the decimal point to the left by the number of places indicated by the exponent.
Q: How do I handle zeros in scientific notation?
A: When writing numbers in scientific notation, you can have zeros before or after the decimal point, but not both. For example, 0.000456 is a valid number in scientific notation, but 0.0000456 is not.
Q: Can I have a decimal point in the exponent in scientific notation?
A: No, you cannot have a decimal point in the exponent in scientific notation. The exponent must be a whole number.
Q: How do I convert a number from scientific notation to a different base?
A: To convert a number from scientific notation to a different base, you need to convert the number to standard notation first, and then convert the standard notation to the desired base.
Q: Can I use scientific notation with fractions?
A: Yes, you can use scientific notation with fractions. In this case, you need to multiply the fraction by 10 raised to the power of the number of places you moved the decimal point.
Examples of Converting Numbers to Scientific Notation
Q: How do I convert 0.000456 to scientific notation?
A: To convert 0.000456 to scientific notation, you need to move the decimal point to the right until you have a number between 1 and 10. Then, you multiply the number by 10 raised to the power of the number of places you moved the decimal point.
Step 1: Move the decimal point to the right until you have a number between 1 and 10
0.000456 → 4.56 (moved the decimal point 4 places to the right)
Step 2: Write the number in scientific notation
The number 0.000456 in scientific notation is 4.56 × 10^(-4).
Q: How do I convert 0.0000009 to scientific notation?
A: To convert 0.0000009 to scientific notation, you need to move the decimal point to the right until you have a number between 1 and 10. Then, you multiply the number by 10 raised to the power of the number of places you moved the decimal point.
Step 1: Move the decimal point to the right until you have a number between 1 and 10
0.0000009 → 9 × 10^(-7) (moved the decimal point 7 places to the right)
Step 2: Write the number in scientific notation
The number 0.0000009 in scientific notation is 9 × 10^(-7).
Conclusion
In conclusion, converting numbers from standard notation to scientific notation and vice versa is an essential skill in chemistry. By understanding how to convert numbers between notations, we can make calculations and comparisons easier.