Functional Skills: Decimals

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Functional Skills: Decimals Revision

Decimals

decimal is any number with a decimal point. Decimals are numbers that lie between whole numbers, e.g. 90.2, 4.57 or 39.41285

There are 5 skills you need to learn for decimals, however they all use methods that you will have previously learned.

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

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Decimal Place Value

The digits after the decimal point also have values. The value decreases the further right you move away from the decimal point.

e.g. the number 39.41285 can be split up into:

 

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Skill 1: Adding Decimals

Adding decimals without a calculator uses the same column method as for whole numbers, you just have to make sure to line up the decimal points.

Example: Calculate 6.436 + 8.992

Use the column method for addition, like below:

Therefore,

6.436 + 8.992 = \textcolor{red}{15.428}

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Skill 2: Subtracting Decimals

Subtracting decimals without a calculator uses the same column method as for whole numbers, you just have to make sure to line up the decimal points and add 0’s to the end of a number (if necessary) so that both numbers have the same number of decimal places.

Example: Calculate 567.63 - 92.478

Use the column method for subtraction like below, adding a 0 so that both numbers have 3 decimal places:

Therefore,

567.63 - 92.478 = \textcolor{red}{475.152}

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Skill 3: Multiplying Decimals

To multiply decimals without a calculator, use the following steps:

Step 1: Convert the decimals to whole numbers by moving the decimal point to the right.

Step 2: Take note of how many decimal places that were moved in total.

Step 3: Complete the column method or grid method for multiplying without a calculator.

Step 4: Move the same number of decimal places back at the end. Now you have the final answer.

 

Example: Calculate 7.68 \times 2.5

The decimal point is moved one time on 2.5 to make it 25 and two times on 7.68 to make it 768. So, 3 decimal places were moved altogether.

Now, use the column method as seen below (or the grid method):

Finally, move the decimal point back the same number of times as before. So, move it 3 times to the left.

The final answer is therefore:

7.68 \times 2.5 = 19.200 = \textcolor{red}{19.2}

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Skill 4: Dividing Decimals

To divide decimals without a calculator, use the following steps:

Step 1: Write the division as a fraction.

Step 2: Multiply the top and bottom by 10 until the bottom is no longer a decimal.

Step 3: Complete the bus stop method for dividing numbers without a calculator.

Step 4: This gives the final answer.

 

Example: Calculate 9.184 \div 1.4

Write the division as a fraction:

9.184 \div 1.4 = \dfrac{9.184}{1.4}

Multiply the top and bottom by 10 until the bottom is no longer a decimal:

\dfrac{9.184 \times 10}{1.4 \times 10} = \dfrac{91.84}{14}

Use the bus stop method to calculate the division:

So,

9.184 \div 1.4 = \textcolor{red}{6.56}

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Skill 5: Comparing Decimals

You can compare and order decimals, just like you can order numbers. However, ordering decimals is a little harder.

To order decimals, you need to look at each number in turn and compare them starting with the first digit.

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

1.101, \,\,\, 0.11, \,\,\, 1.10,  \,\,\, 0.01

 

Step 1: Look at the first digit of each number and compare them.

\xcancel{\textcolor{red}{1}.101}, \,\,\, \overset{\downarrow}{\textcolor{red}{0}}.11, \,\,\, \xcancel{\textcolor{red}{1}.10},  \,\,\, \overset{\downarrow}{\textcolor{red}{0}}.01

2 numbers start with 1 and 2 numbers start with 0. Since we want the smallest first, we can eliminate the 2 largest.

Step 2: Now, look at the second digits of each of the remaining numbers and compare them.

\xcancel{0.\textcolor{red}{1}1}, \,\,\, 0.\overset{\downarrow}{\textcolor{red}{0}}1

The second digit for the first number is a 1 and for the second number it is a 0, so the first number it is bigger, so we can eliminate this.

So, the smallest number is 0.01 and 0.11 is the second smallest.

Step 3: Then, look at the other numbers that were previously crossed out, and compare these.

\xcancel{1.{\textcolor{red}{1}} {\textcolor{blue}{0}}{\textcolor{limegreen}{1}}}, \,\,\,\, 1.{\textcolor{red}{1}}{\textcolor{blue}{0}}

Look at the second digit for each number and compare them, but these are the same. So, compare the third digit, but these again are the same.

The first number has a fourth digit, but the second number does not, so eliminate the first number since it is bigger.

So, 1.10 is the third smallest and 1.101 is the biggest.

Step 4: Finally, write down the correct order:

0.01, \,\,\,\, 0.11, \,\,\,\, 1.10, \,\,\,\, 1.101

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Functional Skills: Decimals Example Questions

a) The 6 is in the third column after the decimal point, which is the thousandths column. So, it is

 

\text{six thousdandths} or \dfrac{6}{1000}

 

b) the numbers are the same until the thousandths column. The first number has a 6 in the thousandths column, where as the second number has a 7 in the thousandths column.

Therefore, 5.0470 is bigger than 5.0461

Use the column method for addition:

\begin{array}{r}81. 070\\+ 31.862\\\hline 112.932 \\\hline 1\,\,\,\,\,\,\,\,1\,\,\,\,\,\, \end{array}

Turn the division into a fraction,

18.63 \div 2.3 = \dfrac{18.63}{2.3}

 

Multiply the top and bottom by 10 until the bottom is no longer a decimal:

 

\dfrac{18.63 \times 10}{2.3\times 10} = \dfrac{186.3}{23}

 

Now, use the bus stop method,

\begin{array}{c}\;\;\;\;\;\;\;\;\;\;\;\;\;8\;.\;1\\23\overline{\left) \cancel1^1\cancel8^{18}6\;.{}^23\right.}\\\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\end{array}

So,

18.63\div 2.3 =  8.1

Move the decimal point to the right of the numbers:

Move the decimal point 3 times on 3.566 to make it 3556

14 does not need changing.

So, there have been 3 decimal places moved in total.

Then, use column multiplication (or grid multiplication),

\begin{array}{r}3566\\\times14\\\hline14264\\+35660\\\hline49924 \end{array}

 

Finally, move the decimal point 3 times to the left, to get the final answer:

 

3.566 \times 14  = 49.924

Use the column method for subtraction:

\begin{array}{r}7.473\\-5.261\\\hline 2.212\end{array}

Additional Resources

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Functional Skills: Decimals Worksheet and Example Questions

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