Significant Figures in Mathematics

Questions and Answers

When performing addition, how should the result be rounded?

To the nearest whole number.

To two decimal places regardless of the measurements.

To the same number of decimal places as the measurement with the most decimal places.

To the same number of decimal places as the measurement with the least decimal places. (correct)

Which of the following is true regarding leading zeros?

They are significant only in whole numbers.

They are only significant if followed by a decimal point.

They are never significant. (correct)

They are always significant.

In the number 0.00450, how many significant figures are present?

3 (correct)

When rounding a number, if the first digit to be removed is 4, what should be done?

Keep the last significant figure the same. Signup and view all the answers

What are the significant figures in the scientific notation number $7.230 imes 10^5$?

4 Signup and view all the answers

Which of the following counts as significant figures?

0.0500, which has 3 significant figures. Signup and view all the answers

Which of the following statements about trailing zeros is correct?

Trailing zeros are significant when they follow a non-zero digit and a decimal point. Signup and view all the answers

If a measurement is taken as 12.56 cm and another as 12.5 cm, what should the result be for their sum?

25.1 cm Signup and view all the answers

Study Notes

Significant Figures In Calculations

Addition/Subtraction:
- The result should have the same number of decimal places as the measurement with the least decimal places.
Multiplication/Division:
- The result should have the same number of significant figures as the measurement with the least significant figures.

Rules For Counting Significant Figures

Non-zero digits are always significant.
Leading zeros (zeros before the first non-zero digit) are not significant.
Captive zeros (zeros between non-zero digits) are significant.
Trailing zeros (zeros at the end of a number) are significant only if there is a decimal point.
Exact numbers (like counts or defined quantities) have an infinite number of significant figures.

Rounding With Significant Figures

If the first digit to be removed is less than 5: round down (retain the last significant figure).
If the first digit to be removed is 5 or greater: round up (increase the last retained significant figure by one).
Carrying through calculations: Keep one extra significant figure until the final result is obtained, then round.

Scientific Notation And Significant Figures

Numbers in scientific notation have significant figures indicated by the digits in the coefficient.
The exponent does not affect the number of significant figures.
Example: In ( 4.56 \times 10^3 ), there are three significant figures (4, 5, and 6).

Significant Figures in Calculations

Addition and subtraction require the result to mirror the decimal places of the measurement with the fewest decimal places.
For multiplication and division, the result should reflect the number of significant figures in the measurement with the least significant figures.

Rules for Counting Significant Figures

Non-zero digits are always considered significant in a number.
Leading zeros, which appear before the first non-zero digit, do not count as significant.
Captive zeros, positioned between non-zero digits, are counted as significant figures.
Trailing zeros are only significant if there is a decimal point present in the number.
Exact numbers, such as defined quantities or counts, are understood to have an infinite number of significant figures.

Rounding with Significant Figures

When rounding, if the digit following the last significant figure is less than 5, retain the last significant figure.
If the digit following the last significant figure is 5 or greater, round up, increasing the last retained significant figure by one.
During calculations, it is advisable to keep one extra significant figure until the final result is determined, then apply rounding.

Scientific Notation and Significant Figures

In scientific notation, the significant figures are determined by the digits in the coefficient.
The exponent in scientific notation does not affect the count of significant figures.
For example, ( 4.56 \times 10^3 ) comprises three significant figures: 4, 5, and 6.

Description

Test your understanding of significant figures in calculations, including addition, subtraction, multiplication, and division. This quiz will also cover the rules for counting significant figures and proper rounding techniques. Perfect for students looking to strengthen their math skills!