Write each of the following in scientific notation:
b. 1440

Verified step by step guidance

1. Identify the significant digits in the number 1440. These are the non-zero digits, which are 1, 4, 4, and 0.
2. Determine where the decimal point would be placed to express the number in scientific notation. In this case, the decimal point should be placed after the first significant digit, making it 1.440.
3. Count the number of places the decimal point was moved to reach its new position. For 1440, the decimal point was moved 3 places to the left.
4. Express the number in the form \( a \times 10^n \), where \( a \) is the number with the decimal point placed after the first significant digit (1.440), and \( n \) is the number of places the decimal point was moved (3).
5. Write the final expression as \( 1.440 \times 10^3 \), which is the scientific notation for 1440.

Key Concepts

Scientific Notation

Scientific notation is a method of expressing numbers that are too large or too small in a compact form. It is written as the product of a number between 1 and 10 and a power of ten. For example, the number 1440 can be expressed as 1.44 x 10^3, where 1.44 is the coefficient and 10^3 indicates that the decimal point in 1.44 is moved three places to the right.

Significant Figures

Significant figures are the digits in a number that contribute to its precision. In scientific notation, the coefficient should be expressed with the appropriate number of significant figures based on the original number. For 1440, if it is known to have three significant figures, it should be written as 1.44 x 10^3, ensuring that the precision of the original number is maintained.

Powers of Ten

Powers of ten are used in scientific notation to indicate the scale of the number. Each power of ten represents a factor of ten multiplied by itself a certain number of times. In the case of 1440, the exponent in 10^3 shows that the number is scaled up by three factors of ten, which helps in quickly understanding the magnitude of the number.