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Place value

Reading scales

This topic is relevant for:

Here we will learn about **rounding **including how to round a number to the nearest

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

**Rounding **is when we approximate numbers in order to make them easier to deal with. We need to round down or up depending on which value is nearer.

There are several ways we can be asked to round a number.

E.g.

** 1478.27** can be rounded in several ways

**Rounding to the nearest ones place,**10, 100 and1000 1478.47 is1478 rounded to the nearest ones place1478.47 is1480 rounded to the nearest10 1478.47 is1500 rounded to the nearest100 1478.47 is1000 rounded to the nearest1000 **Rounding to significant figures**1478.47 is1000 rounded to1 significant figure1478.47 is1500 rounded to2 significant figures1478.47 is1480 rounded to3 significant figures**Rounding to decimal places**1478.2735 is1478.3 rounded to1 decimal place (the nearest tenth)1478.2735 is1478.27 rounded to2 decimal places (the nearest hundredth)1478.2735 is1478.274 rounded to3 decimal places (the nearest thousandth)

**Truncating **a number and **estimation **are also linked with rounding:

**Truncation**is cutting a number off at a certain value with no need to round up.**Estimation**is using the approximated numbers for a calculation; we do not use the exact numbers.

In order to round a number:

**Identify the number to the right of the place value column you are rounding to****If it is a 4 or less we round down, if it is a 5 or more we round up****Write the answer.**

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

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

DOWNLOAD FREERound

**Identify the number to the right of the place value column you are rounding to**

We are rounding to the nearest

This is a 2.

2 **If it is a 4 or less we round down, if it is a 5 or more we round up**

It is a

3 **Write the answer.**

**380**

**Step by step guide: **Rounding to the nearest 10, 100 and 1000

Round

** Identify the number to the right of the place value column you are rounding to **

We are rounding to

This is a 6

** If it is a 4 or less we round down, if it is a 5 or more we round up **

**Write the answer.**

**14.8 **

**Step by step guide:** Decimal places

Round

** Identify the number to the right of the place value column you are rounding to **

We are rounding to the nearest whole number so we identify the number to the right of the 5 in the ones column.

This is a 6.

** If it is a 4 or less we round down, if it is a 5 or more we round up **

**Write the answer.**

**26**

** Se e also: **Decimals

Round

** Identify the number to the right of the place value column you are rounding to **

We are rounding to

This is a 5

** If it is a 4 or less we round down, if it is a 5 or more we round up **

As the digit is a

**Write the answer.**

**400**

**Step by step guide: **Significant figures

Round

** Identify the number to the right of the place value column you are rounding to **

We are rounding to

This is an 8.

** If it is a 4 or less we round down, if it is a 5 or more we round up **

**Write the answer.**

**7.6**

**See also:** Upper and lower bounds

Truncate

** Identify the number in the place value column you are truncating to **

We are truncating to

This is an 8.

**Round the number to what is asked for. Round down or up as required.**

As we have been asked to truncate the number we can miss off all of the digits after the second decimal place.

**Write the answer.**

**94.58**** **to

**Step by step guide: **Truncation

**See also: **Error intervals

Estimate the following calculation:

** Identify the number to the right of the place value column you are rounding to **

As we are estimating we need to round each number to** 1 significant figure**.

In

This is an 8.

In

This is a 4.

** If it is a 4 or less we round down, if it is a 5 or more we round up **

8 is more than 5 so we round 287.1 up to 300.

4 is less than 5 so we round 14.7 down to 10.

**Write the answer.**

The estimated calculation is

The estimated answer is is **3000**

**Step by step guide:** Estimation

**Remember to put zero in as a place holder before the decimal point**

E.g.

When we round

NOT 27

**Sometimes we need a zero in as a place holder with decimal numbers**

E.g.

When we round

**Estimation of numbers within square roots**

If your estimation involves a square root symbol, round those numbers to the nearest square number.

E.g.

\[13.45 + \sqrt{23.6} \approx10 + \sqrt{25} = 10 +5 = 15\]

1. Round 193 to the nearest 100 .

100

200

1

2

We are rounding to the nearest 100 . Identifying the 9 in the tens column indicates we need to round up.

2. Round 13.782 to 2 decimal places.

13.79

13.78

13.780

13.00

We are rounding to 2 decimal places. The 2 in the thousandths column indicates that we should round down.

3. Round 5692 to 2 significant figures.

5600

6000

5700

5690

We are rounding to 2 significant figures. The 9 in the tens column indicates we round up. We need to have zeros in the tens and ones columns as place holders.

4. Round 0.0365 to 2 significant figures.

0.03

0.3

0.036

0.037

We are rounding to 2 significant figures. The second significant figure is 6 .

The 5 in the ten thousandths column indicates we round the 6 up.

5. Truncate 78 to the nearest 10 .

78

70

80

7

We locate the digit in the tens column and truncate to this degree of accuracy, replacing the digit in the ones column with a zero.

6. Estimate 341 × 27 .

9207

9000

6800

9200

By first rounding each number to one significant figure, the calculation becomes

300\times30 = 9000

1. Write 78 348 correct to the nearest 1000 .

**(1 Mark)**

Show answer

78 000

** (1)**

2. (a) Write 8400 correct to one significant figure.

(b) Write 3.51 correct to one significant figure.

**(2 Marks)**

Show answer

(a)

8000

** (1)**

(b)

4

** (1)**

3. Work out an estimate for

\frac{572\times213}{36} .

**(2 Marks)**

Show answer

For rounding one original number to 1 significant figure 600 or 200 or 40

\frac{600\times200}{40}

** (1)**

For the calculation involving all three correctly rounded numbers.

** (1)**

for the correct answer

= 3000

** (1)**

4. (a) Use your calculator to work out

\frac{65.4+49.3}{23.4-15.8}

Write down all the figures on your display.

(b) Write your answer to part (a) to 1 decimal place.

**(2 Marks)**

Show answer

(a) 15.092105…

** (1)**

** **

(b) 15.1 (1.d.p)

** (1)**

You have now learned how to:

- Round numbers to a number of decimal places
- Round numbers to a number of significant figures
- Use approximation through rounding to estimate answers

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