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Place value

Rounding to the nearest 10, 100 and 1000 Decimal places Significant figuresThis topic is relevant for:

Here we will learn about **truncation** including how to truncate numbers to powers of 10, decimals and significant figures.

There are also truncation worksheets based on Edexcel, AQA and OCR exam questions, along with further guidance on where to go next if you’re still stuck.

**Truncation **is shortening a number at a particular place value and filling in any zeros to keep it the same size.

Truncation can be thought of as rounding down to a given degree of accuracy.

To do this we write the figures of the number up to and including the place value required and then, if necessary write zeros to make the number the same size as the original number.

E.g.

38621 truncated to the 1000s

= 38000

4.7392 truncated to 2.d.p

= 4.73

39.8573 truncated to 1 significant figure

=30

In order to truncate a number:

**Step 1: Locate the figure for the degree of accuracy required.**

**Step 2: Write the figures (including a decimal place if present) up to and including the degree of accuracy.**

**Step 3: If the degree of accuracy is 10 or more, fill in zeros to make the number the correct size.**

Get your free truncation worksheet of 20+ questions and answers. Includes reasoning and applied questions.

DOWNLOAD FREEGet your free truncation worksheet of 20+ questions and answers. Includes reasoning and applied questions.

DOWNLOAD FREETruncate 47.893 to an integer.

1**Locate the figure for the degree of accuracy required.**

In 47.893, the units figure is **7**

2**Write the figures (including a decimal place if present) up to and including the degree of accuracy.**

47

3**If the degree of accuracy is 10 or more, fill in zeros to make the number the correct size.**

There are no zeros required so the truncated value is 47.

Truncate 2.45789 to 2 decimal places.

**Locate the figure for the degree of accuracy required.**

In 2.45789, the second decimal place is **5**.

**Write the figures (including a decimal place if present) up to and including the degree of accuracy.**

2.45

**If the degree of accuracy is 10 or more, fill in zeros to make the number the correct size.**

There are no zeros required so the truncated value is 2.45.

Truncate 3468 to the hundreds.

**Locate the figure for the degree of accuracy required.**

In 3468, the hundreds figure is **4**

**Write the figures (including a decimal place if present) up to and including the degree of accuracy.**

34

**If the degree of accuracy is 10 or more, fill in zeros to make the number the correct size.**

The degree of accuracy is 100, which has two zeros. Therefore, we need to write two zeros to make the number the correct size.

The truncated value is 3400.

Truncate 26783 to one significant figure.

**Locate the figure for the degree of accuracy required.**

In 26783, the first significant figure is **2**.

**Write the figures (including a decimal place if present) up to and including the degree of accuracy.**

2

**If the degree of accuracy is 10 or more, fill in zeros to make the number the correct size.**

The degree of accuracy is 10000, which has four zeros. Therefore, we need to write four zeros to make the number the correct size.

The truncated value is 20000.

**The truncated number is not the correct size**

It is common for step 3 to be missed and a number such as 3547 to be truncated to 35 to 2 significant figures. It is important that the zeros are written to make the number the correct size.

**The number is rounded up instead of truncated**

It is common to round up instead when the number after the figure being truncated to is 5 or more.

Truncation is part of our series of lessons to support revision on rounding numbers, and upper and lower bounds. You may find it helpful to start with the main rounding numbers lesson for a summary of what to expect, or use the step by step guides below for further detail on individual topics. Other lessons in this series include:

1. Truncate 0.0368 to 1 significant figure

3

0.3

0.03

0.04

The first significant figure is 3. There are no zeros required so the answer is 0.03.

2. Truncate 6.256 to the units

6

7

6.2

6256

The units figure is 6. There are no zeros required so the answer is just 6.

3. Truncate 28.985 to 1 decimal place

29.0

28.9

28.98

28.99

The first decimal place is 9. There are no zeros required so the answer is 28.9.

4. Truncate 21835 to the thousands

21000

22000

21800

21835

The thousands figure is 1. There are three zeros required so the answer is 21000.

5. Truncate 3269 to 3 significant figures

3270

3269

3260

3300

The third significant figure is 6. There is one zero required so the answer is 3260.

6. Truncate 4.396836 to 3 decimal places

4.397

4.396

4.000

4.390

The third decimal place is 6. There are no zeros required so the answer is4.396.

1. Truncate 2.7868 to 2 decimal places

**(1 mark)**

Show answer

` 2.78 `

**(1)**

2. (a) x is truncated to the tens and given as 400 . What the the largest possible integer value of x ?

(b) y is truncated to the hundreds and given as 2700 . What the the largest possible integer value of y ?

**(2 marks)**

Show answer

409

**(1)**

**(1)**

3. A rectangle has a length 6.487m and a width 3.924m . By truncating the measurements to 10cm , approximate the area of the rectangle

**(3 marks)**

Show answer

6.4 or 3.9

**(1)**

**(1)**

**(1)**

You have now learned how to:

- Apply and interpret limits of accuracy when truncating

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