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Expert-verified Found in: Page 18 ### Physics Principles with Applications

Book edition 7th
Author(s) Douglas C. Giancoli
Pages 978 pages
ISBN 978-0321625922 # 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?

The significant figures of the given numbers are (a) 3, (b) 4, (c) 3, (d) 1, (e) 2, (f) 4, and (g) 2.

See the step by step solution

## Step 1. Meaning of significant figures

Significant figures give the exact count of digits in a number. For determining the number of significant figures, zeros are treated as place holders.

## Step 2. Steps for the determination of the number of significant figures

• Excluding zero, consider all integers as significant figures.
• If there is a zero between two non-zero digits of a number, it is also considered a significant figure.
• If there are zeros in a decimal number, they are considered significant figures regardless they come before or after the decimal.

For example, in the number 0.045, there are two significant figures. Here, zero is not considered a significant figure as it is a place value holder.

## Step 3. Determination of the number of significant figures in (a) 214

In the number 214, the total count of digits is three. Thus, there are three significant figures in this number.

## Step 4. Determination of the number of significant figures in (b) 81.60

In the given number, zero is a significant figure as it comes after a non-zero digit (6). Thus, there are four significant figures in the number 81.60.

## Step 5. Determination of the number of significant figures in (c) 7.03

In the given number, zero is a significant figure as it is present in between two non-zero digits. Thus, there are three significant digits in the number 7.03.

## Step 6. Determination of the number of significant figures in (d) 0.03

The zeros before a decimal number and before a non-zero digit are not significant. In this case, there is one digit, excluding zero.

Thus, there is one significant figure in 0.03.

## Step 7. Determination of the number of significant figures in (e) 0.0086

The zeros before a decimal number and before a non-zero digit are not significant. In this case, there are two digits, except zero.

Thus, there are two significant figures in 0.0086.

## Step 8. Determination of the number of significant figures in (f) 3236

The total number of digits in the number 3236 is four. Thus, there are four significant figures in 3236.

## Step 9. Determination of the number of significant figures in (g) 8700

All zeros after any non-zero number are not significant figures.

The number 8700 has two zeros after non-zero digits. Thus, it has only two significant figures. ### Want to see more solutions like these? 