Lesson 3: Rounding to Significant Figures

Objective

At the end of the lesson, students should be able to:

• Give approximations to specified numbers of significant figures (S.F).

Numbers can also be approximated to a given number of significant figures (sf). We often use significant figures (sf) when we want to approximate a number with a lot of digits in it.

In the number 63.42 the 6 is the most significant figure as it has a value of 60. In contrast, the 2 is the least significant as it only has a value of 2 hundredths.

The steps taken to round a number to a given number of significant figures (sf) are very similar to those used for rounding to a given number of decimal places;

• From the left, count the digits. If you are rounding to 2 significant figures (sf), count 2 digits, for 3 significant figures (sf), count three digits and so on. When the original number is less than one, start your counting from the first non- zero digit.
• Look at the next digit to the right. When the value of this next digit is less than 5, leave the digit you counted to the same. However if the value of the next digit is equal to or greater than 5, add one to the digit you counted.
• Ignore all other digits, but put in enough zeroes to keep the number the right size or value.

Example 1

Write 0.0023 to 1sf.

Solution

In example, only two numbers have any significance (ie the 2 and the 3). The 2 is the most significant so we start our counting from the first non- zero digit. Observe that the next digit after 2 is 3 which less than 5. We therefore run down to get 0.0023.

Therefore 0.0023 is written as 0.002 to 1 sf.

Example 2

Write 69.28 to 3 sf.

Solution

The three most significant numbers are 6, 9 and 2. However the fourth number needs to be considered to see whether the third number is to be rounded up or down. The fourth number is 8, therefore we round up to get 69.3

Therefore 69.28 is written as 69.3 to 3 sf.

Example 3

Write 48599 to 1 sf.

Solution

The most significant number is 4 and the next number is 8. We round it up and the rest of the numbers become zeroes.

Therefore 48599 is written as 50000 to 1 sf.

Unit 9 lesson 3: Exercise 1

Write the following to the number of significant figures written in the brackets.

1. 9642 (1sf)
2. 925 (3sf)
3. 99 (1sf)
4. 67 (3sf)
5. 087 (2sf)
6. 41952 (3sf)
7. 2045 (2sf)
8. 399 (1sf)
9. 089 (2sf)
10. 57123 (1sf)

Unit 9 lesson 3: Exercise 2

Round each of the following to the number of significant figures (sf) indicated.

1. 00973 (1sf)
2. 7538 (2sf)
3. 7 (1sf)
4. 9 (1sf)
5. 658 (2sf)
6. 732 (1sf)
7. 6 (2sf)
8. 942 (1sf)
9. 98 (1sf)
10. 00305 (2sf)