Question

How many significant figures do each of the following numbers have: (a) 214, (b) 81.60, (c) 7.03, (d) 0.03, (e) 0.0086, (f) 3236, and (g) 8700?

Answer 1

The number of significant figures in the numbers provided are three for 214, four for 81.60, three for 7.03, one for 0.03, two for 0.0086, four for 3236, and two to four for 8700 depending on the presence of a decimal point.

Step-by-step explanation:

The number of significant figures in a number reflects how precisely it is known. Here is the count for each of the numbers you've provided:

• (a) 214 has three significant figures.
• (b) 81.60 has four significant figures because zeros after the decimal point are significant.
• (c) 7.03 has three significant figures.
• (d) 0.03 has one significant figure because leading zeros to the left of non-zero digits are not significant.
• (e) 0.0086 has two significant figures, the zeros before 86 are not significant as they are only placeholders.
• (f) 3236 has four significant figures.
• (g) 8700 has two significant figures if it's not written with a decimal point (e.g., 8700.), indicating that the zeros are not measured but estimated. With a decimal point (8700.) it would have four significant figures.

Remember, trailing zeros in a whole number without a decimal point are not considered significant unless otherwise indicated. For measurements with a decimal point, all trailing zeros are significant when they follow a non-zero digit.

Answer 2

In determining the number of significant figures in a given number, there are three rules to always remember / follow:

First: All integers except zero are always significant.

Second: Any zeros located between non zeroes are always significant.

Third: A zero located after a non zero in a decimal is always significant whether it is before or after the decimal

Therefore using this rule, the number of significant digits in the given numbers are:

(a) 214 = 3

(b) 81.60 = 4

(c) 7.03 = 3

(d) 0.03 = 1

(e) 0.0086 = 2

(f) 3236 = 4

(g) 8700 = 2