Functional Skills: Ordering Numbers

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Functional Skills: Ordering Numbers Revision

Ordering Numbers

When ordering numbers, they can either go from smallest to largest (ascending order) or largest to smallest (descending order). You may be asked to order positive and negative numbers.

Positive numbers with more digits are larger, and negative numbers with more digits are smaller.

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

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Ordering Large Numbers

You may also be asked to order large numbers. To order large numbers look at each number in turn and compare the digits, starting with the first.

Example: Put the following numbers in order from largest to smallest.

3456, \,\,\, 5364, \,\,\, 3465, \,\,\ 5634

 

Step 1: Split the numbers into positive and negative. There are only positive numbers here, so we do not need to do this.

Step 2: Put the numbers into groups with the same number of digits. They all have 4 digits, so we do not need to do this.

Step 3: Look at the first digit for each number and compare them:

\xcancel{\textcolor{blue}{3}456}, \,\,\, \overset{\downarrow}{\textcolor{blue}{5}}364, \,\,\, \xcancel{\textcolor{blue}{3}465},  \,\,\, \overset{\downarrow}{\textcolor{blue}{5}}634

2 numbers start with 3. Since we are looking for the largest first, we can eliminate those 2 numbers.

Step 4: Look at the second digits.

5 \xcancel{\textcolor{blue}{3}64}, \,\,\,  5\overset{\downarrow}{\textcolor{blue}{6}}34

6 is bigger than 3, so eliminate the first number.

So, 5634 is the largest and 5364 is the second largest.

Step 5: Look at the other numbers.

3 \xcancel{\textcolor{blue}{4}\textcolor{red}{5}6}, \,\,\,  3 \textcolor{blue}{4}\overset{\downarrow}{\textcolor{red}{6}} 5

The second digit is the same in each number, so compare the third digit. 6 is bigger than 5 so eliminate the first number.

So, 3465 is the third largest and 3456 is the smallest.

Step 6: Finally, write down the correct order:

5634, \,\,\, 5364, \,\,\, 3465, \,\,\, 3456

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Ordering Negative Numbers

When ordering negative numbers, you need to be careful – for negative numbers, the bigger the number after the minus (-) sign, the smaller the negative number.

Example: Put the following numbers in order from largest to smallest.

23, \,\,\, -23, \,\,\, 32, \,\,\, -32

 

Step 1: Split the numbers into positive and negative.

23, \,\,\, 32     and    -23, \,\,\, -32

Step 2: Put the numbers into groups with the same number of digits. They all have 2 digits, so we do not need to do this.

Step 3: Then, look at the first digit for each number and compare them.

\xcancel{\textcolor{blue}{2}3}, \,\,\,  \overset{\downarrow}{\textcolor{blue}{3}}2

3 is greater than 2, so 32 is the largest and 23 is the second largest.

Step 4: Now, look at the negative numbers and compare the first digit of each.

- \overset{\downarrow}{\textcolor{blue}{2}}3, \,\,\,  - \xcancel{\textcolor{blue}{3}2}

-3 is smaller than - 2, since the bigger the number after the minus sign, the smaller the negative number.

So, -23 is the third largest and -32  is the smallest.

Step 5: Finally, write down the correct order:

32, \,\,\, 23, \,\,\, -23, \,\,\, -32

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Example: Smallest to Largest

Write these numbers in order from smallest to largest.

470,\,\,\, 316,\,\,\,54,\,\,\,46,\,\,\,486

[1 mark]

Splitting the numbers up into groups with the same number of digits, gives

54, \,\,\, 46     and     470, \,\,\, 316, \,\,\, 486

Comparing the first digits of the numbers with 2 digits,

46 is smaller than 54

Then, comparing the first digits of the numbers with 3 digits,

316 is the smallest

Now, comparing the second digits of the remaining numbers with 3 digits,

470 is smaller than 486

This gives the final answer to be,

46,\,\,\,54,\,\,\,316,\,\,\,470,\,\,\,486

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Functional Skills: Ordering Numbers Example Questions

Comparing the first digits,

11022 and 11012 are smaller than 22101 and 22011

Then, comparing the rest of the digits,

11012 is smaller than 11022

and

22011 is smaller than 22101

So, the correct order is:

11012, \,\,\, 11022, \,\,\, 22011, \,\,\, 22101

Splitting the numbers up into negative and positive,

-665, \,\,\, -565     and    656, \,\,\, 556

Comparing the first digits,

-565 is bigger than -665

and

656 is bigger than 556

So, the correct order is:

-665, \,\,\,\, -565, \,\,\,\,556, \,\,\,\, 656

Splitting the numbers up into negative and positive,

-12, \,\,\, -2     and    8, \,\,\, 5

Comparing the first digits,

-12 is smaller than -2

and

8 is bigger than 5

So, the correct order is:

-12, \,\,\,\, -2, \,\,\,\,5, \,\,\,\, 8

Additional Resources

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Exam Tips Cheat Sheet

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PFS

Formula Booklet

FS Level 2

Functional Skills: Ordering Numbers Worksheet and Example Questions

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Ordering Numbers L1, L2

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