Significant Digits - George Brown College

Significant Digits

Significant digits are widely used in science to communicate the preciseness of a measurement. The more significant digits a stated measurement has, the more precise it is.

1. Which digit(s) in a number are significant?

Rule All non-zero digits (i.e. digits from 1 to 9) are significant. Zero digit(s) located between two non-zero digits are significant.

Zero digit(s) located to the right of a decimal point is/are significant.

Example 14.5 has three significant digits. All the digits in this number are significant. 10.05 has four significant digits. The digits 1 and 5 are significant because they are non-zero digits. The two 0s are significant because they are located between two non-zero digits. 98.0 has three significant digits. The digits 9 and 8 are significant because they are non-zero digits. The 0 is significant because it's located to the right of the decimal point.

Zero digit(s) located to the left of significant digits is/are NOT significant.

TIP: A good way to remember this rule is that without the 0, the value of the number would remain the same (i.e. 98 is the same value as 98.0). The reason for including the trailing 0 is to show that it's significant. 0.0067 has two significant digits. The digits 6 and 7 are significant because they are non-zero digits. The 0s are NOT significant because they are located to the left of the significant digits 6 and 7.

Zero digit(s) located to the right of other significant digits in the whole number part is/are NOT significant.

TIP: In this case the 0s are included to show the value (i.e. how small) the number (measurement) is. The 0s do NOT show us the preciseness of this measurement. The 0s are simply place holders. 9800 has three significant digits. The digits 9 and 8 are significant because they are non-zero digits. The 0s are NOT significant because they are in the whole number part of this number and are to the right of significant digits.

A zero digit with a dot underneath the zero is significant.

TIP: Again, the 0s are included to show the value (i.e. how large) the number (measurement) is. The 0s do NOT show us the preciseness of this measurement. The 0s are simply place holders.

95000

Tutoring and Learning Centre, George Brown College 2014

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This number has four significant digits. The digits 9 and 5 are significant because they are non-zero digits. The zero with the dot underneath is significant. The zero between 5 and the 0 with the dot underneath is also significant because it's located between two significant digits.

Practice Question:

1. For each measurement below state the number of significant digits it has. a) 53.409 b) 1.20 c) 0.0038 d) 90000 e) 4307 f) 105000.0 g) 0.00809

Answer: 1. a) five e) four

b) three f) seven

c) two g) three

d) one

2. Operations with Significant Digits

Operations with measurements can change the number of significant digits the final answer has. The following rules should be followed when rounding the final answer to the correct number of significant digits:

- For adding and subtracting, round the final answer to the least number of decimal places in the measurements being added or subtracted.

Note: If you are adding or subtracting whole numbers, round to the same number of significant digits as the least precise measurement.

- For multiplying and dividing, round the final answer to the least number of significant digits in the measurements being multiplied or divided.

- For multiple operations, perform the entire calculation carrying all the digits. Then, determine the number of significant digits or decimal places at EACH step (following the correct order of operations). It is helpful to underline the "extra" decimal places or significant digits being carried to the next step. Round the final answer to the same number of significant digits or decimal places as the least precise component of the calculation..

Tutoring and Learning Centre, George Brown College 2014

georgebrown.ca/tlc

Examples:

1. Perform each calculation and round to the correct number of significant digits.

a) 14.578 + 34.2 =

b) 54.76 ? 1.999 =

c) 58.31 ? 2.5 =

d) 0.054 x 19.3 =

32.09 + 1.2 -17.035

e)

=

19.8

Solutions: 1. a) 14.578 + 34.2 = 48.778 Round to one decimal place. Final answer is 48.8

b) 54.76 ? 1.999 = 52.761 Round to two decimal places. Final answer is 52.76

c) 58.31 ? 2.5 = 23.324 Round to two significant digits. Final answer is 23

d) 0.054 x 19.3 = 1.0422 Round to two significant digits. Final answer is 1.0

e) 32.09 + 1.2 -17.035 =

19.8

Step 1: 32.09 + 1.2 = 33.29 The intermediate answer should have one decimal place.

Step 2: 33.29 ? 17.035 = 16.255 The intermediate answer should have one decimal place.

Step 3: 16.255 ? 19.8 = 0.820959596... The answer is rounded to three significant digits.

The final answer is 0.821.

Tutoring and Learning Centre, George Brown College 2014

georgebrown.ca/tlc

Practice Exercises:

1. Perform each calculation and round to the correct number of significant digits.

a) 87.654 + 123.9 = b) 98.36 ? 5.8 = c) 348.72 x 0.0506 = d) 205.06 ? 19.2 + 48.001 = e) 78.32 ? 2.1 x 193 = f) 90.3 x 1.2 + 5.84 = g) 73.2+18.72 x 6.1 =

3.4

h) 123.45 + 7.6 x 100.3 =

5.1

Answers: 1. a) 211.6 b) 17 c) 17.6 d) 233.9 e) 7200 f) 110 g) 55 h) 790

Tutoring and Learning Centre, George Brown College 2014

georgebrown.ca/tlc

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