Suma y resta en notación científica

Vitual

13 Feb 201407:39

Summary

TLDRThe video explains how to perform addition and subtraction using scientific notation. It emphasizes the importance of aligning the exponents of base 10 before performing operations. The process involves adjusting one term's exponent to match the other, moving decimal points accordingly. Several examples are provided, illustrating how to convert numbers to scientific notation, perform operations, and return results in proper notation. The lesson highlights key concepts like adjusting decimal points, dealing with negative exponents, and ensuring the final result falls within the correct range for scientific notation.

Takeaways

🔢 To add or subtract in scientific notation, the exponents of base 10 must be the same.
🔄 You can adjust one term by converting its exponent to match the other, such as converting 10^3 to 10^5.
⚖️ When changing the exponent, adjust the decimal point accordingly to maintain the original value.
➕ After aligning the exponents, you can perform the addition or subtraction of the coefficients.
📏 In scientific notation, the coefficient must be a number between 1 and 10.
📉 Moving the decimal point left increases the exponent, while moving it right decreases the exponent.
✖️ When multiplying terms in scientific notation, adjust for the decimal shifts based on the exponents.
➖ To subtract terms with different exponents, align the exponents first, then subtract the coefficients.
💡 After subtraction, ensure the result remains in proper scientific notation by adjusting the decimal point if necessary.
📝 In all operations, remember to adjust the decimal based on the differences in exponents for accurate scientific notation results.

Q & A

What needs to be equal for adding or subtracting in scientific notation?
-The exponents of the base 10 must be equal before performing addition or subtraction in scientific notation.
How can you make the exponents of 39.12 x 10^3 and 32.4 x 10^5 equal?
-You can convert 39.12 x 10^3 to 0.3912 x 10^5 by adjusting the decimal point and increasing the exponent by 2.
What happens when you add or subtract numbers in scientific notation with unequal exponents?
-You must first adjust one of the numbers so that the exponents are equal before performing the operation.
How do you adjust the decimal point when converting 39.12 x 10^3 to match the exponent of 10^5?
-You move the decimal point two places to the left, converting 39.12 x 10^3 into 0.3912 x 10^5.
What is the result of adding 0.3912 x 10^5 and 32.4 x 10^5?
-The sum is 32.7912 x 10^5.
How do you convert 0.0005 to scientific notation?
-Move the decimal point three places to the right, giving you 5 x 10^-4.
What is the difference between 5 x 10^-3 and 0.8 x 10^-3?
-The difference is 4.2 x 10^-3.
How do you subtract 232.47 x 10^-4 from 12.90081 x 10^-5?
-First, adjust 232.47 x 10^-4 to 23.247 x 10^-5 to make the exponents equal, then subtract to get 23.011719 x 10^-5.
How do you convert 23.011719 x 10^-5 to proper scientific notation?
-Move the decimal point three places to the left, resulting in 2.3011719 x 10^-2.
What is the final result of adding 1.48 x 10^6 and 3 x 10^8 in scientific notation?
-After converting 1.48 x 10^6 to 0.0148 x 10^8, the sum is approximately 3.0148 x 10^8.

Outlines

00:00

🔢 Introduction to Scientific Notation Addition

This section explains how to perform addition in scientific notation, focusing on aligning the exponents of the base 10. Two numbers are given, one with an exponent of 3 and another with 5. The goal is to convert the exponents to be equal, choosing to adjust the term with the exponent 3 by adding 2 to match the exponent 5. This requires moving the decimal point two places to the left, converting the number accordingly. Once the exponents are equal, the two values can be added, resulting in a sum of 2.79 × 10^5.

05:03

✖️ Conversion of Numbers to Scientific Notation

This paragraph explains how to convert regular numbers into scientific notation by adjusting the decimal point. A decimal is shifted three places to convert 0.0005 into 5 × 10^-3. The conversion is further clarified by demonstrating how to align the terms for subtraction, ensuring both are written with the same exponent, −3 in this case. After aligning the terms, the subtraction is performed, resulting in 4.2 × 10^-3.

➖ Subtraction in Scientific Notation

In this part, subtraction in scientific notation is tackled. Two terms, 232.47 × 10^-4 and 12.90081 × 10^-5, are given, and the goal is to make the exponents equal by converting the first term to 10^-5. This involves shifting the decimal point one place to the right, which results in 2300.24.7. After aligning the exponents, the two terms are subtracted, yielding a result of 2300.11.719 × 10^-5.

🔄 Final Adjustments in Scientific Notation

This section concludes the earlier subtraction by ensuring the result adheres to the rules of scientific notation. The final value, 2300.11.719 × 10^-5, is adjusted by moving the decimal point three places to the left, resulting in 2.30011 × 10^-2. The process of adjusting the exponent from −5 to −2 by adding 3 is explained.

🔬 Adding Large Numbers in Scientific Notation

This final example demonstrates the addition of large numbers in scientific notation. The first number, 1.48 million, is converted to scientific notation by shifting the decimal eight places to the left, giving 1.48 × 10^8. The second number, 3 × 10^8, remains as is. After aligning the terms, the numbers are added to yield 3.0148 × 10^8.

Mindmap

Keywords

💡Scientific Notation

Scientific notation is a method of expressing very large or very small numbers by using powers of 10. In the video, it is crucial because all the calculations involve converting numbers into this format to perform operations like addition and subtraction. For example, '39.12 x 10^3' is converted to '0.3912 x 10^5' to match the exponents.

💡Exponents

Exponents refer to the power to which a number is raised, indicating how many times the base (in this case, 10) is multiplied by itself. In the video, matching exponents is essential for addition and subtraction in scientific notation, as shown when converting '10^3' to '10^5' by adjusting the decimal point.

💡Decimal Movement

Decimal movement involves shifting the decimal point to either the left or right to adjust the number when changing its exponent in scientific notation. For instance, in the video, moving the decimal two places to the left transforms '39.12 x 10^3' into '0.3912 x 10^5', making the exponents consistent.

💡Addition in Scientific Notation

When adding numbers in scientific notation, the exponents of the base 10 must be the same. The video explains how to adjust one of the terms by converting '10^3' into '10^5' to make them compatible for addition. After aligning the exponents, the numbers are added directly, such as adding '0.3912' and '2.4'.

💡Subtraction in Scientific Notation

Similar to addition, subtraction in scientific notation requires matching the exponents. The video illustrates this when subtracting '5 - 0.8', both terms multiplied by '10^-3'. The video emphasizes ensuring both terms have the same power of 10 before performing the subtraction.

💡Base 10

Base 10 is the foundation of the decimal system, used in scientific notation to express large or small numbers compactly. In the video, base 10 is used throughout all examples, such as converting '50.0008' into '5 x 10^-3'. Understanding base 10 is essential for performing operations in scientific notation.

💡Aligning Exponents

Aligning exponents refers to the process of making the exponents of two terms in scientific notation equal, so operations like addition or subtraction can be performed. In the video, this process involves adjusting the decimal and changing exponents, as seen when aligning '10^3' with '10^5' to make them compatible.

💡Moving the Decimal Point

In scientific notation, moving the decimal point is a method used to adjust the number while keeping the notation valid. For example, shifting the decimal point three places to the left turns '2,324.7 x 10^-4' into '2.3247 x 10^-1', aligning it with the other term for subtraction.

💡Rounding

Rounding numbers is often necessary in scientific notation to maintain significant figures without losing accuracy. The video shows this during the addition and subtraction processes, where final results are sometimes rounded, as seen in the sum '2.79 x 10^5'.

💡Multiplying by Powers of 10

Multiplying by powers of 10 is a core operation in scientific notation. The video demonstrates this when converting numbers like '1,480,000' to '1.48 x 10^6'. Understanding how multiplying by powers of 10 shifts the decimal point is crucial for performing calculations in scientific notation.

Highlights

To add or subtract in scientific notation, the exponents of base 10 must be the same.

When the exponents are different, one term must be converted to match the other.

In the first example, 39.12 * 10^3 is converted to 0.3912 * 10^5 to match the exponent of 10^5.

Once the exponents are equal, the coefficients can be added directly, resulting in 2.7912 * 10^5.

To convert numbers to scientific notation, move the decimal point until the coefficient is between 1 and 10.

In the second example, 0.000008 becomes 8.0 * 10^-6 after moving the decimal six places to the right.

Subtracting numbers in scientific notation follows the same rule of matching exponents before performing the operation.

In the third example, 232.47 * 10^-4 is converted to 23.247 * 10^-3 to match the exponent of 10^-3.

The subtraction results in 11.719 * 10^-5, which is then adjusted to 1.1719 * 10^-4.

Final answers in scientific notation should always have a coefficient between 1 and 10.

For large numbers, like 1,480,000, converting to scientific notation involves moving the decimal six places to get 1.48 * 10^6.

In the final example, 1.48 * 10^6 is added to 3 * 10^8 by converting 1.48 to match the exponent of 10^8.

When converting, add zeros in place of missing digits when moving the decimal point.

After converting, the sum of 0.0148 and 3 results in 3.0148 * 10^8.

Scientific notation simplifies calculations by ensuring all terms have the same base-10 exponent before operations are performed.