Question
Unit 4 study guide: scientific notation
Answers
GPT 3.5
Scientific notation is a way of expressing very large or very small numbers in a more concise and manageable format. It is commonly used in scientific and mathematical calculations.
1. How to write a number in scientific notation:
- Move the decimal point to the right or left so that there is only one non-zero digit to the left of the decimal point.
- The number of places you moved the decimal point determines the exponent of 10.
- If the decimal point is moved to the left, the exponent is positive. If it is moved to the right, the exponent is negative.
- Write the number in the format: a x 10^b, where a is the non-zero digit and b is the exponent.
2. How to convert a number from scientific notation to standard notation:
- Multiply the non-zero digit (a) by 10 raised to the power of the exponent (b).
- If the exponent is positive, move the decimal point to the right. If it is negative, move it to the left.
3. Addition and subtraction in scientific notation:
- The numbers must have the same exponent in order to perform addition or subtraction.
- If the exponents are different, adjust the numbers by moving the decimal point and adjusting the exponent accordingly.
- Once the exponents are the same, perform the desired operation on the non-zero digits and keep the exponent the same.
4. Multiplication in scientific notation:
- Multiply the non-zero digits together.
- Add the exponents of 10.
- Adjust the non-zero digit and exponent if necessary to ensure that the number is in proper scientific notation.
5. Division in scientific notation:
- Divide the non-zero digits.
- Subtract the exponent of the denominator from the exponent of the numerator.
- Adjust the non-zero digit and exponent if necessary to ensure that the number is in proper scientific notation.
6. Applications of scientific notation:
- Scientific research: Expressing very large or very small measurements, such as distances in space or microscopic structures.
- Engineering: Working with measurements of complex systems, such as electrical circuits or structural designs.
- Financial calculations: Expressing very large or very small monetary values, such as national debts or company revenues.
Remember to use significant figures when using scientific notation, and be aware of the appropriate number of decimal places in the final answer.
1. How to write a number in scientific notation:
- Move the decimal point to the right or left so that there is only one non-zero digit to the left of the decimal point.
- The number of places you moved the decimal point determines the exponent of 10.
- If the decimal point is moved to the left, the exponent is positive. If it is moved to the right, the exponent is negative.
- Write the number in the format: a x 10^b, where a is the non-zero digit and b is the exponent.
2. How to convert a number from scientific notation to standard notation:
- Multiply the non-zero digit (a) by 10 raised to the power of the exponent (b).
- If the exponent is positive, move the decimal point to the right. If it is negative, move it to the left.
3. Addition and subtraction in scientific notation:
- The numbers must have the same exponent in order to perform addition or subtraction.
- If the exponents are different, adjust the numbers by moving the decimal point and adjusting the exponent accordingly.
- Once the exponents are the same, perform the desired operation on the non-zero digits and keep the exponent the same.
4. Multiplication in scientific notation:
- Multiply the non-zero digits together.
- Add the exponents of 10.
- Adjust the non-zero digit and exponent if necessary to ensure that the number is in proper scientific notation.
5. Division in scientific notation:
- Divide the non-zero digits.
- Subtract the exponent of the denominator from the exponent of the numerator.
- Adjust the non-zero digit and exponent if necessary to ensure that the number is in proper scientific notation.
6. Applications of scientific notation:
- Scientific research: Expressing very large or very small measurements, such as distances in space or microscopic structures.
- Engineering: Working with measurements of complex systems, such as electrical circuits or structural designs.
- Financial calculations: Expressing very large or very small monetary values, such as national debts or company revenues.
Remember to use significant figures when using scientific notation, and be aware of the appropriate number of decimal places in the final answer.