# Unit 2 Section 2 : Decimals and Place Value

In this section we will look at the place values to the right of the decimal point.
In the example questions, work out the answer then click to see whether you are correct.

## Place values for decimals

The number 1.743 can be broken into four parts: Example
What is the value of the '6' in the number 2.164? ## Sorting Decimals

We can sort decimal numbers into order, just like we can sort whole numbers.
Imagine we want to sort these numbers: 0.5, 0.95, 0.905, 0.59, 0.6, 0.9

Comparing these numbers is easier if we write all the numbers with the same number of decimal places.
Now we have: 0.500, 0.950, 0.905, 0.590, 0.600, 0.900

The extra "0"s on the end make no difference to the value of the number, but they are easier to compare.
We can now see that sorting these numbers gives: 0.500, 0.590, 0.600, 0.900, 0.905, 0.950

After removing the extra "0"s, the final answer is: 0.5, 0.59, 0.6, 0.9, 0.905, 0.95

Example
Sort these numbers into order:
0.7, 0.27, 0.72, 0.702, 0.207, 0.2 ## Rounding to a certain number of decimal places

If we want to round 4.732 to 2 decimal places, it will either round to 4.73 or 4.74. 4.732 rounded to 2 decimal places would be 4.73 (because it is the nearest number to 2 decimal places).
4.737 rounded to 2 decimal places would be 4.74 (because it would be closer to 4.74).
4.735 is halfway between 4.73 and 4.74, so it is rounded up: 4.735 rounded to 2 decimal places is 4.74.

Examples
(a) What is 5.79 rounded to 1 decimal place. (b) What is 3.242 rounded to 2 decimal places? ## Exercises

Work out the answers to the questions below and fill in the boxes. Click on the button to find out whether you have answered correctly. If you are right then will appear and you should move on to the next question. If appears then your answer is wrong. Click on to clear your original answer and have another go. If you can't work out the right answer then click on to see the answer.

Question 1
What is the value of the "5" in each of the numbers below? Give your answer as a decimal.

(a) 0.45  (b) 0.54  (c) 5.74  (d) 3.415  (e) 4.258  Question 2
Write the numbers below in order, smallest first. Separate your answers with commas, like this : 0.85, 0.9, 0.8, 0.58, 0.6, 0.5, 0.87  Question 3
Write each of the numbers below correct to one decimal place.

(a) 1.47  (b) 3.68  (c) 0.45  (d) 3.751  (e) 4.08  Question 4
Write each of the numbers below correct to two decimal places.

(a) 3.444  (b) 8.555  (c) 0.321  (d) 4.7612  (e) 0.3002  Question 5
Write these numbers in descending order, largest first.

0.7, 0.2991, 1.05, 1.508, 0.58, 2.4  Question 6
You are given the digits 3, 4, 0, 7 and the decimal point.
Each digit must be used only once, and the decimal point must appear between two digits.

(a) What is the largest number you can make?  (b) What is the smallest number you can make?  You have now completed Unit 2 Section 2
 Your overall score for this section is Correct Answers You answered questions correctly out of the questions in this section. Incorrect Answers There were questions where you used the Tell Me button. There were questions with wrong answers. There were questions you didn't attempt.
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Produced by A.J. Reynolds January 2001