Dividing scientific notation
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Scientific notation is a way to write very large or small numbers in their simplest form. It involves writing a number as the product of a coefficient and a power of 10. To divide numbers in scientific notation, you divide the coefficients, subtract the exponents, shift the decimal if needed to keep the coefficient between 1 and 10, and write the result with the new exponent. Some examples of dividing numbers in scientific notation are worked out step-by-step. The document also provides practice problems for dividing numbers in scientific notation and examples of using scientific notation to solve real-world problems involving distances and speeds.
Dividing scientific notation
- 2. Scientific notation is the way of expressing very large or very small numbers in easiest form. Writing the numbers in the form a x 10ᵑ of is called Scientific Notation which is also known as Exponential Notation. Scientific Notation has the following terms • Co-efficient • Base • Exponent
- 3. Scientific Notation should always have a base 10 and the base number 10 is always written in exponent form. The number 123, 000, 000, 000 in scientific notation is written as; 1.23 x 10¹¹ The first number 1.23 is called the co- efficient. It must be greater than or equal 1 and less than 10. The second number is the base. It must always be 10 in scientific notation. The base number 10 is always written in exponent form. In the number 1.23 x 10¹¹ the number 11 is referred to as the exponent or power of ten.
- 4. How to divide scientific notation ? Step 1: Divide the coefficient. Step 2: Subtract exponent of the base (power of 10) Step 3: Write the number with the subtracted new exponent. Step 4: Check if the resulting number is less than 1, shift the decimal point to the right & then decrease the power according to the decimal places shifted. Step 5: Write the result in scientific notation.
- 5. Question 1: Divide (0.23 x 1011) by (2.6 x 104) Solution: Step 1: Divide the coefficient. 0.23 ÷ 2. = 0.08846 Step 2: Subtract the exponent of the base 10 11 – 4 = 7 Step 3: Write the number with the subtracted new exponent 0.08846 x 10⁷ Step 4: Now the decimal number is less than 1, so right shift the decimal point by 2 places and decrease the power by 2 0.08846 x 10⁷ = 8.846 x 10⁵ Step 5: Write the result in scientific notation. Hence, dividing scientific notation (0.23 x 1011) by (2.6 x) we get 8.846 x 10⁵
- 6. Question 2: Divide 3.4 x 10 -3 by 5 x 10 6 Solution : Step 1: Divide the coefficient. 3.4 ÷ 5 = 0.68 Step 2: Subtract the powers of the base 10. - 3 – 6 = - 9 Step 3: Write the number with the subtracted new exponent. 0.68 x 10⁻⁹ Step 4: Now the decimal number is less than 1, so right shift the decimal point by 1 places and decrease the power by 1. 0.68 x 10⁻⁹ = 6.8 x 10 ⁻¹⁰ Step 5: Write the result in scientific notation. Hence, dividing scientific notation ( 3. 4 x 10 ⁻ᶟ) by ( 5 x 10⁻⁶) we get 6.8 x 10 ⁻¹⁰
- 7. Try this: 1. (9 x 10⁻⁶)/(3 x 10⁻ᶟ) 2. (2 x 10ᶟ) ÷ (4 x 10⁸) 3. 4. (3 x 10⁻⁶) ÷ ( 2 x 10⁻⁴) 5. (7 x 10⁻⁵)/(2 x 10¹⁰)
- 8. Problems: 1.) What is the ratio of Milky Way radius to our solar system radius given that, the distance from Pluto to Sun is 5.9 x 10¹² meters and the Milky Way disk radius is 3. 9 x 10²⁰ meters. Round the coefficient to the nearest tenth. 2.) The speed of light is 3 x 10⁸ meters/seconds. If the sun is 1.5 x10¹¹ meters from the Earth, how many seconds does it take light to reach the earth?