An electric kettle uses 378,000 joules of energy to boil 1 liter of water. Express this energy using correct scientific notation. [tex]$[?] \times 10^{[?]} \text { joules }$[/tex] Enter the coefficient for the first blank and the exponent for the second blank. Coefficient (green)
Answer (2)
Convert the number to scientific notation.
Move the decimal point until the number is between 1 and 10, which gives the coefficient.
Count the number of places the decimal was moved, which gives the exponent of 10.
Express the number in scientific notation: 3.78 × 1 0 5 .
Explanation
Understanding the Problem We are given that an electric kettle uses 378,000 joules of energy to boil 1 liter of water. Our goal is to express this amount of energy in scientific notation. Scientific notation is a way of writing numbers as a product of a number between 1 and 10 (the coefficient) and a power of 10.
Finding the Coefficient To convert 378,000 to scientific notation, we need to express it in the form a × 1 0 n , where 1 ≤ a < 10 and n is an integer. To find a , we move the decimal point in 378,000 to the left until we have a number between 1 and 10. In this case, we move the decimal point 5 places to the left to get 3.78.
Determining the Exponent Since we moved the decimal point 5 places to the left, the exponent n is 5. Therefore, we can write 378,000 as 3.78 × 1 0 5 .
Final Answer Thus, the energy used by the electric kettle, expressed in scientific notation, is 3.78 × 1 0 5 joules.
Examples
Scientific notation is extremely useful in many fields, especially in physics and chemistry, where you often deal with very large or very small numbers. For example, the speed of light is approximately 3.0 × 1 0 8 meters per second, and the mass of an electron is approximately 9.11 × 1 0 − 31 kilograms. Using scientific notation makes these numbers easier to write and compare. In everyday life, you might encounter scientific notation when dealing with large amounts of money or very small measurements in manufacturing or engineering.
The energy of 378,000 joules can be expressed in scientific notation as 3.78 × 1 0 5 joules. The coefficient is 3.78 and the exponent is 5. This format simplifies the representation of large numbers.
;
