# Functional Skills: Rounding and Estimating

## Functional Skills: Rounding and Estimating Revision

**Rounding Numbers**

**Rounding** is a way of changing a number to make it easier to write and work with, even though it may be less exact. Rounding can be done to a number of **decimal places** (d.p.) or **to the nearest whole number, or nearest 10, etc.**

If you **round numbers too early**Â during a calculation, then the final answer may be wrong, so only round at the **end** of a calculation, unless the question specifically asks you to round before.

There are **5** skills you need to learn in this topic.

Make sure you are happy with the following topics before continuing.

**Skill 1: Rounding to a Number of Decimal Places**

**Example:** Round 17.268 to **2 decimal places**.

**Step 1:** Find the digit you are rounding to. In this case it is the 2nd digit after the decimal point.

17.2\textcolor{red}{6} 8

**Step 2:** If the number to the right is below 5, we round down and it stays the same. If it is 5 or more, we round up and increase it by 1.

8 is bigger than 5, so the 6 increases by 1 to 7

**Step 3:** Don’t write down and digits after this. What it remaining is the final answer, which is

17.2\textcolor{red}{7}

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**Skill 2: Rounding to the Nearest Whole Number**

**Example:** Round 53.182 to **the nearest whole number**.

**Step 1:** Find the digit you are rounding to. In this case it is the first digit before the decimal point, since we are rounding to the nearest whole number.

5\textcolor{orange}{3}.182

**Step 2:** If the number to the right is below 5, we round down and it stays the same. If it is 5 or more, we round up and increase it by 1.

1 is smaller than 5, so the 3 stays the same.

**Step 3:** Don’t write down any digits after this, including the decimal point. What it remaining is the final answer, which is

5\textcolor{orange}{3}

**Skill 3: Rounding to the Nearest 10**

**Example:** Round 365 to **the nearest ten**.

**Step 1:** The first digit, 3, is in the hundreds column, but the second digit, 6, is in the tens column, so this is the digit we are rounding to.

3\textcolor{orange}{6}5

**Step 2:** If the number to the right is below 5, we round down and it stays the same. If it is 5 or more, we round up and increase it by 1.

5 is 5 or more, so the 6 is increased by 1 to 7.

**Step 3:** Finally, change all of the digits after this to \textcolor{limegreen}{0}‘s. What it remaining is the final answer, which is

3\textcolor{orange}{7}\textcolor{limegreen}{0}

**Skill 4: Rounding to the Nearest 100**

**Example:** Round 4179 to **the nearest hundred**.

**Step 1:** The first digit, 4, is in the thousands column, but the second digit, 1, is in the hundreds column, so this is the digit we are rounding to.

4\textcolor{orange}{1}79

**Step 2:** If the number to the right is below 5, we round down and it stays the same. If it is 5 or more, we round up and increase it by 1.

7 is 5 or more, so the 1 is increased by 1 to 2.

**Step 3:** Finally, change all of the digits after this to \textcolor{limegreen}{0}‘s. What it remaining is the final answer, which is

4\textcolor{orange}{2}\textcolor{limegreen}{00}

**Note:** We use similar techniques to round to the nearest 1000, 10000, etc.

**Skill 5: Estimating**

Answers to calculations can be **estimated** by **rounding** the numbers in them to the nearest whole number, or nearest 10, etc. This can be used to check your calculations are correct or estimate the answer without a calculator.

**Example:** Stevie sells some items on an auction website.

She sells a TV for Â£178.50, a microwave for Â£32.85 and a hairdryer for Â£27.10

**Estimate** how much money Stevie makes from selling these items.

Since the value of the items are all in the tens or hundreds, it would be better to round them all to the nearest 10.

Â£178.50 rounds to \textcolor{purple}{Â£180}

Â£32.85 rounds to \textcolor{purple}{Â£30}

Â£27.10 rounds to \textcolor{purple}{Â£30}

So, in total she makes

\textcolor{purple}{Â£180} + \textcolor{purple}{Â£30}+ \textcolor{purple}{Â£30} = \textcolor{purple}{Â£240}

**Notes:**

- If the digit you are rounding is a \textcolor{blue}{9}, you have to round it up to 0 and add 1 to the digit to the left.
- Usually, you will not be told what to round the numbers to when you are estimating – you just need to use your common sense. However, there is normally not a right or wrong answer when estimating – you will be given leeway.

## Functional Skills: Rounding and Estimating Example Questions

**Question 1:** Round 44.1099 to 3 decimal places.

**[1 mark]**

Here, we are rounding to 3 decimal places, so look at the 3rd digit after the decimal point, which is the first 9.

44.10\overset{\downarrow}{9}9

9 (the second one) is bigger than 5, so the first 9 is rounded up and 1 is added.

However, this makes 10, so we need to change this to 0 and carry the 1 to the left and add it to that column.

Donâ€™t write down any digits after this.

So,

44.1099 rounded to 3 decimal places is 44.110

**Question 2:** Round 570182 to the nearest thousand.

**[1 mark]**

Here, we are rounding to the nearest thousand, so look at the 3rd digit, which is the 0.

57\overset{\downarrow}{0}182

1 is smaller than 5, so we round down and the 0 stays the same.

Make the rest of the digits after this zero.

So,

570182 rounded to the nearest thousand is 570000

**Question 3:** Round 913.78 to the nearest whole number.

**[1 mark]**

Here, we are rounding to the nearest whole number, so look at the 1st digit before the decimal point, which is the 3.

91\overset{\downarrow}{3}.78

7 is bigger than 5, so we round up and the 3 increases by 1 to 4.

Do not write down any digits after this, including the decimal point.

So,

913.78 rounded to the nearest whole number is 914

**Question 4:** Mr Singh runs a triathlon made up of three sections. He completes the first section in 48 minutes, the second section in 82 minutes and the third section in 59 minutes.

Estimate how long it takes Mr Singh to complete the triathlon, in minutes.

**[1 mark]**

Since the times of each section are all in the tens, it would be better to round them all to the nearest 10.

48 rounds to 50

82 rounds to 80

59 rounds to 60

So, in total he completes the triathlon in

50 + 80 + 60 = 190 minutes

**Question 5:** The surface area of a sphere is given by the formula A = 4\pi r^2, where A is the surface area and r is the radius of the circle.

Estimate the surface area of a sphere, in cm^2, where \pi = 3.14 and r = 4.92 cm.

**[2 marks]**

Since the numbers are in the units, we should round them both to the nearest whole number.

3.14 rounds to 3

4.92 rounds to 5

So, the surface area of the sphere is

4 \times 3 \times 5^2 = 4 \times 3 \times 25 = 300 cm^2

## Functional Skills: Rounding and Estimating Worksheet and Example Questions

### Rounding and Estimating EL3

Entry Level 3NewOfficial PFS### Rounding and Estimating L1, L2

FS Level 1FS Level 2NewOfficial PFS[responsive-flipbook id=”pfs_pocket_revision_guide_-_sample”]

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