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Place value

Decimals Rounding to the nearest 10, 100, 1000 Decimal placesThis topic is relevant for:

Here we will learn about significant figures including how to round numbers to one significant figure, two significant figures and three significant figures.

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

**Significant figures **are the digits in a number that contribute to the accuracy of it.

We start counting significant figures at the **first non-zero digit of a number** which is called the first significant figure, the next digit is then called the second significant figure and so on.

A significant figure could be to the left of the decimal point or the right of the decimal point.

E.g.

Rounding numbers to significant figures (often abbreviated to sig figs or s.f.) is similar to rounding to a number of decimal places, units, tens, hundreds and thousands but in this case we need to find the appropriate significant figure to give the correct degree of accuracy.

In order to round to a given number of significant digits:

- Locate the significant figure for the degree of accuracy required. The first non-zero digit is the first significant figure.
- Look at the next digit to the right. Is it
5 or more? - If it is
5 or more – round up by adding1 to the previous digit.

If it is less than5 – round down by keeping the previous digit the same.

If the degree of accuracy is10 or more, fill in zeros to make the number the correct size.

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

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

DOWNLOAD FREERound

**Locate the significant figure for the degree of accuracy required. The first non-zero digit is the first significant figure.**

**3**692

The first non-zero digit is the

2**Look at the next digit to the right. Is it 5 or more?**

**3¦6**92

3**If it is 5 or more – round up by adding 1 to the previous digit. If it is less than 5 – round down by keeping the previous digit the same. If the degree of accuracy is 10 or more, fill in zeros to make the number the correct size.**

As

** 4000** to

Round

**Locate the significant figure for the degree of accuracy required. The first non-zero digit is the first significant figure.**

**0**39

The first non-zero digit is the

**Look at the next digit to the right. Is it 5 or more?**

**70¦3**9

**If it is 5 or more – round up by adding 1 to the previous digit. If it is less than 5 – round down by keeping the previous digit the same. If the degree of accuracy is 10 or more, fill in zeros to make the number the correct size.**

As

** 0.070** to

It is important to keep the zero after the seven as it must be given to two significant figures.

Round

**Locate the significant figure for the degree of accuracy required. The first non-zero digit is the first significant figure.**

**7**53

The first non-zero digit is the

**Look at the next digit to the right. Is it 5 or more?**

**2**4.**7¦5**3

The digit to the right is

**If it is 5 or more – round up by adding 1 to the previous digit. If it is less than 5 – round down by keeping the previous digit the same. If the degree of accuracy is 10 or more, fill in zeros to make the number the correct size.**

As it is a

**24.8**

**Assuming the first zeros are significant**

A common error is to think the first zeros in a number like

**Assuming all zeros are not significant**

A common error is to think that all zeros in a number like

**Leaving out zeros to make the number the correct size**

It is important to remember to fill in the zeros if the degree of accuracy is more than

Round 76340 to one significant figure.

8

70000

80000

8000

The first significant figure is the 7 . The next digit to the right is 6 , which is bigger than 5 , so we round up. Adding 1 to 7 gives us 8 and filling in the zeros gives us 80000 .

2. Round 0.3897 to one significant figure.

0.3

0.4

0

1

The first significant figure is the 3 . The next digit to the right is 8 , which is bigger than 5 , so we round up. Adding 1 to 3 gives us 4 therefore the answer is 0.4 .

3. Round 26460 to two significant figures.

25000

27000

26

26000

The first significant figure is 2 and the second is 6 . The next number to the right is 4 , which is less than 5 , so we round down. The 6 remains the same and filling in the zeros gives us 26000 .

4. Round 78.56 to two significant figures.

78.6

78

79

80

The first significant figure is 7 and the second is 8 . The next number to the right is 5 , so we round up. Adding one to the 8 gives us 9 and therefore we have 79 .

5. Round 4.7041294 to three significant figures.

4.70

4.704

4.71

5.70

The third significant figure is 0 . The next figure to the right is 4 , which is less than 5 . Therefore we round down and the 0 remains the same. The answer is 4.70 to 3 s.f.

6. Round 0.0051489 to three significant figures.

0.005

0.00515

0.00514

0.00525

The first significant figure is 5 and the third significant figure is 4 . The next number to the right is 8 , which is bigger than 5 , so we round up. Adding 1 to the 4 gives us 5 and therefore we have 0.00515 .

1. (a) Write 467983 correct to two significant figures.

(b) Write 0.03887 correct to one significant figure.

(c) Write 60.7328 correct to three significant figures.

**(3 marks)**

Show answer

470000

**(1)**

**(1)**

**(1)**

2. Sam was finding the area of a compound shape. His calculated result was 60942.937 cm^{2}. He needs to round this area to two significant figures, choose the correct answer.

60900 cm^{2} 61000 cm^{2} 60942.94 cm^{2} 60000 cm^{2}

**(1 mark)**

Show answer

61000cm^{2}

3. (a) Use a calculator to work out \frac{\sqrt{6.79}}{3.72-2.81} . Write down all of the digits on your calculator screen.

(b) Round your answer to part (a) to three significant figures.

**(3 marks)**

Show answer

(a) Finding intermediate results of 2.605 … or 0.91 from the subtraction seen.

**(1)**

Final result of 2.863475653

**(1)**

(b) Rounded correctly to 2.86

**(1)**

You have now learned how to:

- Apply and interpret limits of accuracy when rounding

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