In Exercises 77–86, write each number in scientific notation. 64,000

Verified step by step guidance

1. Step 1: Understand the concept of scientific notation. Scientific notation is a way to express very large or very small numbers as a product of a number between 1 and 10 and a power of 10. The general form is: $a\; \times \; 10b$, where and $b$ is an integer.
2. Step 2: Identify the given number, which is 64,000. To convert this number into scientific notation, we need to rewrite it as a product of a number between 1 and 10 and a power of 10.
3. Step 3: Move the decimal point in 64,000 to create a number between 1 and 10. The decimal point in 64,000 is initially at the end of the number (64,000.0). Move the decimal point 4 places to the left, resulting in 6.4.
4. Step 4: Count the number of places the decimal point was moved. Since the decimal point was moved 4 places to the left, the exponent of 10 will be 4.
5. Step 5: Combine the number and the power of 10 to write the number in scientific notation. The result is $6.4\; \times \; 104$.

Key Concepts

Scientific Notation

Scientific notation is a way 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 64,000 can be expressed as 6.4 x 10^4 in scientific notation.

Powers of Ten

Powers of ten are used in scientific notation to indicate how many times a number should be multiplied or divided by ten. Each power corresponds to a place value in the decimal system. For instance, 10^4 means 10 multiplied by itself four times, which equals 10,000.

Significant Figures

Significant figures are the digits in a number that contribute to its precision. In scientific notation, only the digits in the coefficient (the number between 1 and 10) are considered significant. For example, in 6.4 x 10^4, the '6' and '4' are significant figures, indicating the precision of the measurement.