Question

Write each number in scientific notation. 0.0514

Short answer

5.14 x 10^{-2}

Step-by-step solution

- Understanding Scientific Notation

Scientific notation is a way to express very large or very small numbers. It is written as the product of a number between 1 and 10 and a power of 10. For example, a number like 5,000 can be written as 5 x 10^3.

- Identify the Decimal Point Location

Identify the location of the decimal point in the given number. The decimal point in 0.0514 is between the first zero and the digit 5.

- Move the Decimal Point

Move the decimal point to the right until you have a number between 1 and 10. In 0.0514, you need to move the decimal point two places to the right to get 5.14.

- Count the Number of Moves

Count the number of places you moved the decimal point. In this case, you moved it 2 places to the right.

- Write the Number in Scientific Notation

Since you moved the decimal point 2 places to the right, you multiply by 10 raised to the power of -2 (because you're dealing with a number less than 1). The scientific notation of 0.0514 is 5.14 x 10^{-2}.

Key concepts

Adding Decimal Points in Numbers

Understanding how decimal points work is essential. The decimal point is a dot used to separate the whole number part from the fractional part. In the number 0.0514, the decimal point is positioned between the first zero and the digit 5. When converting a number to scientific notation, you often need to move this decimal point to get a new number between 1 and 10. For example, in scientific notation, 0.0514 is written as 5.14 x 10^{-2}, where the decimal point was moved two places to the right.

Using Powers of 10 in Calculations

Powers of 10 play a crucial role in scientific notation. A power of 10 means 10 raised to an exponent (like 10^2 or 10^{-3}).The exponent tells you how many times to multiply 10 by itself. For example, 10^3 means 10 x 10 x 10, which is 1000. In scientific notation, we use these powers to make big or very small numbers easier to write and understand. When moving the decimal place to the right or left, the power of 10 helps keep the value the same. When converting 0.0514 to 5.14 x 10^{-2}, the 'minus 2' indicates two decimal places moved to the right.

Expressing Numbers in Different Ways

Expressing numbers in scientific notation is very useful. It simplifies reading and writing extremely large or small numbers. Scientific notation is a method where numbers are expressed as a product of a number between 1 and 10 and a power of 10. This makes it easier to handle and perform calculations without writing out all the zeros. For instance, instead of writing 0.0514, you can express the same number more efficiently as 5.14 x 10^{-2}. This format is particularly beneficial in scientific work and engineering where precision and clarity are important.