Write each number in decimal notation: 7.45*10^(-5)

Verified step by step guidance

1. Understand that the expression $7.45\times {10}^{-5}$ is in scientific notation.
2. The exponent $-5$ indicates that the decimal point in the number $7.45$ needs to be moved 5 places to the left.
3. Start by writing the number $7.45$ and identify the current position of the decimal point, which is between 7 and 4.
4. Move the decimal point 5 places to the left, adding zeros as placeholders for each move.
5. Write the new number in decimal notation after moving the decimal point.

Key Concepts

Scientific Notation

Scientific notation is a way of expressing numbers that are too large or too small in a more manageable form. It is written as a product of a number (the coefficient) between 1 and 10 and a power of ten. For example, 7.45*10^(-5) means 7.45 divided by 100,000, which simplifies calculations and comparisons of very large or small values.

Decimal Notation

Decimal notation is the standard form of writing numbers using digits and a decimal point to separate the whole number part from the fractional part. It allows for precise representation of values, including those that are very small or very large. Converting from scientific notation to decimal notation involves calculating the power of ten and adjusting the decimal point accordingly.

Exponents

Exponents indicate how many times a number, known as the base, is multiplied by itself. In the expression 10^(-5), the base is 10 and the exponent is -5, which means 1 divided by 10 raised to the power of 5, or 1/100,000. Understanding exponents is crucial for manipulating scientific notation and converting it to decimal form.