10 Questions
When performing a combined operation, what determines the number of significant figures in the answer?
The operation with the fewest number of significant figures
What is the purpose of using scientific notation to write very large or small numbers?
To make the numbers more understandable when they are very large or small
What part of the number determines the number of significant digits when using the formula Nx10X?
The number N
When adding 1.71 + 3.11 + 6.31 and then dividing by 1.2, what is the number of significant figures in the answer?
Two
Why is the answer to 11.1 divided by 1.2, approximately 9.3?
Because 1.2 has two significant figures
What is the number of significant figures in the number 1.20x10^-3?
Three
What is the rule for determining the number of significant figures in a number in scientific notation?
Count the number of digits in the coefficient
When using scientific notation, what is not significant in the formula Nx10X?
The 10 and exponent X
What is the purpose of using significant figures in combined operations?
To ensure the answer is as precise as possible
What happens to the number of significant figures when performing a combined operation?
It decreases
Study Notes
What are Significant Digits?
- Significant digits describe the number of digits used to express a calculated or measured quantity.
- Significant digits begin with the first digit to the left and end with the last nonzero digit to the right, typically after a decimal place.
Defining Significant Digits
- Accuracy refers to how close a measured value is to the true or accepted value.
- Precision refers to how close the measurements are to each other.
Understanding the Rules of Significant Digits
- Rule One: All non-zero digits are significant.
- Rule Two: Zeros that appear between non-zero digits are always significant.
- Rule Three: Zeros before a decimal point that precede non-zero digits are not significant.
- Rule Four: Zeros to the right of a decimal after a non-zero number are significant.
- Rule Five: Trailing zeros in a whole number are significant only when there is a decimal.
Rules for Operations
- When adding or subtracting values, the number of significant digits cannot exceed the value with the least number of decimal places.
- When multiplying or dividing numbers, the values you start with must first be significant for all digits, and the result has the same number of significant digits as the values you started with.
Rounding with Significant Digits
- When rounding numbers, we first need to know how many digits are significant.
- Typical rounding rules apply to significant figures (if the number is a 5 or below, the number stays the same, but if the number to the right of the digit is greater than 5, we round up).
Examples of Using Significant Digits
- Subtracting 5.554 and 2.2: the result has only two significant digits, which is 3.3.
- Dividing 18.2 and 1.11: the result has only three significant digits, which is 11.9.
- Rounding the number 1.300061 to 6 significant digits: the result is 1.30006.
Significant Digits in Combined Operations and Exponents
- Combined operations involve more than one operation.
- Exponents are used to write very large or small numbers, and the number of significant figures in N is determined by following the rules.
- Examples of using exponents: 1.2x10^3, 1.20x10^-3, 0.02x10^2, and 00.200x10^-5.
Learn about the concept of significant digits, how to count them, and their importance in scientific measurements and calculations.
Make Your Own Quizzes and Flashcards
Convert your notes into interactive study material.
Get started for free
