# Significant Figures and Rounding Off

Definition: What exactly are significant figures?

The number of significant figures in a result is the number of figures that are known with some degree of reliability. Significant figures are very important when reporting scientific data as the will give the reader an idea of how well you measured your data.

## RULES When Assigning Significant Figures:

- All non-zero (1, 2, 3, 4, 5, 6, 7, 8, 9) digits are ALWAYS significant

Here’s what we mean:

22 has two significant figures

55.3 has three significant figures

14.96 has four significant figures

2. Zeros placed between other digits are always significant

Let’s look at that now:

3005 has four significant figures

208 has three significant figures

3.09 has three significant figures

3. Leading zeros to the left of the first non-zero digits are NOT significant.

They simply indicate the position of the decimal point

For Example:

0.0596 has three significant figures

0.0002 has one significant figure

4. Trailing zeros that are to THE RIGHT OF A DECIMAL POINT in a number ARE SIGNIFICANT

Look at these:

0.0150 has three significant figures

0.200 has three significant figures

0.80 has two significant figures

5. When a number ends in zeros that are not to the right of a decimal point, the zero are not necessarily significant.

To avoid confusions and problems: the use of scientific notation or exponential is used.

For Example:

170 may be two or three significant figures

86,000 may be two or three significant figures

90,200 may be three or five significant figures

So it is recommended that you change the number to exponential and then use that figure to determine how many significant figures are there.

Using or examples above:

1.7 x 10^{-2} has two significant figures

8.6 x 10^{-4} has two significant figures or 8.60 x10^{-4} has three significant figures.

9.02 x 10^{-4} has three significant figures

### Significant figures in Multiplication, Division, Trig. Functions

In a calculation involving multiplication, division, trigonometric function etc., the number of significant digits in the answer should be equal to the least number of significant digits in any one of the numbers being multiplied, divided etc.

Example:

2.13 (3 sig fig) x 4.236(4 sig fig) = 9.02 (the answer has 3 sig figs.)

483 / 68.60 = 7.04

### Significant figures in Addition and Subtraction

When performing addition and subtraction calculations, the number of decimal places in the answer should be the same as the least number of decimal places in any of the numbers in the calculation.

Example:

1.96 + 8.7 = 14.6

48.1 – 32.05 = 16.1

## Rounding Off

(1) If the number to be dropped is greater than 5, the last digit is increased by one.

For example, 11.6 is rounded to 12.

(2) If the number to be dropped is less than 5, the last digit is left as it is.

For example, 10.2 is rounded to 10.

(3) If the number to be dropped is 5, and if any digit following it is not zero, the last remaining digit is increased by one.

For example, 9.52 is rounded to 10.

(4) If the digit to be dropped is 5 and is followed only by zeroes, the last remaining digit is increased by one if it is odd, but left as it is if even.

For example,

13.50 is rounded to 14,

12.5 is rounded to 12.

Now that we’ve examine all the rules and shown examples then using the rules of significant figures and rounding off try these:

- 47.76 + 3.907 + 227.2 =
- 378.26 – 42.970 =
- 104.230 + 25.07795 + 0.70 =
- 122 – 0.25 + 4.109 =
- 2.02 x 3.4 =
- 800.0 / 5.2405 =
- 0.1174 x 418 =
- 48 x 5.00 =
- 5.3
^{4 }= - 0.555 x (85 + 12.3) =

Answers to the Questions above:

- 47.76 + 3.907 + 227.2 = 278.9
- 378.26 – 42.970 = 335.29
- 104.230 + 25.07795 + 0.70 = 130.01
- 122 – 0.25 + 4.109 = 118
- 2.02 x 3.4 = 6.9
- 800.0 / 5.2405 = 152.7
- 0.1174 x 418 = 49.0
- 48 x 5.00 =2.4 x10
^{2} - 5.3
^{4 =}7.9 x 10 - 0.555 x (85 + 12.3) = 54

The only way to master this is by practicing. Just practice and practice and practice some more until you master it. You know what they say : Practice makes perfect!!

Let us know how it goes.