Round each number to three significant figures. a. 79,845.82 b. 1.5148937×10⁷ c. 1.13499999995 d. 0.0000415389

Verified step by step guidance

1. 1. To round a number to three significant figures, you need to look at the fourth digit. If the fourth digit is 5 or more, you round up the third digit. If it's less than 5, you leave the third digit as it is.
2. 2. For 79,845.82, the fourth digit is 8, which is more than 5. Therefore, you round up the third digit, which is 9, to the next number, which is 0. However, since 9 is the maximum digit, you also need to round up the second digit, which is 8, to the next number, which is 9. The result is 80,000.
3. 3. For 1.5148937 * 107, the fourth digit is 8, which is more than 5. Therefore, you round up the third digit, which is 4, to the next number, which is 5. The result is 1.52 * 107.
4. 4. For 1.13499999995, the fourth digit is 9, which is more than 5. Therefore, you round up the third digit, which is 4, to the next number, which is 5. The result is 1.14.
5. 5. For 0.0000415389, the fourth significant digit is 5, which is equal to 5. Therefore, you round up the third significant digit, which is 1, to the next number, which is 2. The result is 0.000042.

Key Concepts

Significant Figures

Significant figures are the digits in a number that contribute to its precision. This includes all non-zero digits, any zeros between significant digits, and trailing zeros in the decimal portion. Understanding how to identify and count significant figures is crucial for rounding numbers accurately.

Rounding Rules

Rounding rules dictate how to adjust numbers to a specified number of significant figures. When rounding, if the digit following the last significant figure is 5 or greater, the last significant figure is increased by one. If it is less than 5, the last significant figure remains unchanged.

Scientific Notation

Scientific notation is a way of expressing numbers that are too large or too small in a compact form, using powers of ten. For example, 1.5148937 * 10^7 is a representation of a large number. Understanding how to manipulate and round numbers in scientific notation is essential for accurate calculations in chemistry.