Significant Figures and Zero (1.3)

Summary

This video explains the rules for determining when zeros in a number are considered significant. It covers three main cases: zeros sandwiched between nonzero digits are always significant, zeros preceding all nonzero digits are never significant, and zeros following nonzero digits are significant only if a decimal point is present. Through multiple examples, the video clarifies how the position of zeros and the presence of a decimal affect the total count of significant figures. Viewers are encouraged to practice with examples to confidently identify significant zeros in various numbers, mastering the concept effectively.

Takeaways

• 😀 Zeros sandwiched between nonzero digits are always significant. Example: 391 has four significant figures.
• 😀 Zeros between nonzero digits are significant regardless of how many zeros there are or where they appear. Example: 109,000 has six significant figures.
• 😀 Zeros coming before nonzero digits (to the left) are never significant. Example: 0.0000491 has three significant figures.
• 😀 Zeros to the left of a decimal point in numbers like 0.0132 are not significant. The significant figures are just the nonzero digits.
• 😀 Zeros after nonzero digits are significant only if there is a decimal point. Example: 83,000 with no decimal point has two significant figures.
• 😀 If there is a decimal point, zeros to the right of nonzero digits are always significant. Example: 83.000 has five significant figures.
• 😀 For numbers like 200 with a decimal point (200.), all zeros are significant. Example: 200. has three significant figures.
• 😀 A number like 50,000 with no decimal point has only two significant figures, and the zeros are not significant.
• 😀 The presence of a decimal point changes how zeros are treated after nonzero digits; they become significant with the decimal.
• 😀 To accurately determine the number of significant figures in a number, always ask: 'Is there a decimal point?'

Q & A

What is the rule for zeros sandwiched between nonzero digits?

Zeros that are located between nonzero digits are always significant. For example, in 109,003, all the zeros between 1, 9, and 3 are significant, giving a total of 6 significant figures.

Are leading zeros significant?

No, zeros that come before all nonzero digits (leading zeros) are never significant. For example, 0.000491 has only 3 significant figures: 4, 9, and 1.

How do trailing zeros after nonzero digits behave without a decimal point?

Trailing zeros after nonzero digits without a decimal point are not significant. For example, 83,000 has only 2 significant figures (8 and 3).

How do trailing zeros after nonzero digits behave with a decimal point?

Trailing zeros after nonzero digits with a decimal point are significant. For example, 83,000. has 5 significant figures because the decimal point indicates the zeros are counted.

How many significant figures are in 0.0132?

There are 3 significant figures in 0.0132: 1, 3, and 2. The leading zeros are not significant.

What is the total number of significant figures in 50.000?

There are 5 significant figures in 50.000 because the decimal point makes all trailing zeros significant.

Why is checking for a decimal point important when determining significant figures?

Checking for a decimal point is important because it determines whether trailing zeros after nonzero digits are significant. Without a decimal, they are not counted; with a decimal, they are counted.

How many significant figures are in 0.000000062?

There are 2 significant figures in 0.000000062: 6 and 2. All leading zeros before 6 are not significant.

Does the number of zeros or groups of zeros matter when they are sandwiched between nonzero digits?

No, neither the number of zeros nor the number of groups of zeros matters. All zeros sandwiched between nonzero digits are significant, regardless of quantity or grouping.

What is the recommended method to master identifying significant figures?

The recommended method is to practice with many examples, analyzing leading, sandwiched, and trailing zeros in different numbers, and applying the decimal point rule consistently.

How many significant figures are in 200.?

There are 3 significant figures in 200. because the decimal point makes all trailing zeros significant.

How many significant figures are in 32,100 without a decimal?

There are 5 significant figures in 32,100. Since the number has no decimal point, only the nonzero digits and any sandwiched zeros are counted.