Converting Between Decimals & Fractions

Test yourself

Converting Between Simple Fractions and Decimals

One half

$\large\frac{1}{2}$ is the same as 0.5.
- $\large\frac{1}{2}$ is the same as 0.5 because 1 whole is the same as 100 'hundredths'.
- $\large\frac{1}{2}$ of 100 'hundredths' is 50 'hundredths' which is the same as 0.5.

One quarter

$\large\frac{1}{4}$ is the same as 0.25.
- $\large\frac{1}{4}$ is the same as 0.25 because 1 whole is the same as 100 'hundredths'.
- $\large\frac{1}{4}$ of 100 'hundredths' is 25 'hundredths' which is the same as 0.25.

One fifth

$\large\frac{1}{5}$ is the same as 0.2.
- $\large\frac{1}{5}$ is the same as 0.2 because 1 whole is the same as 100 'hundredths'.
- $\large\frac{1}{5}$ of 100 'hundredths' is 20 'hundredths' which is the same as 0.2.

Two fifths

$\large\frac{2}{5}$ is 2 lots of $\large\frac{1}{5}$ .
- $\large\frac{1}{5}$ = 0.2
- $\large\frac{2}{5}$ = 0.2 × 2 = 0.4

Four fifths

$\large\frac{4}{5}$ is 4 lots of $\large\frac{1}{5}$ .
- $\large\frac{1}{5}$ = 0.2
- $\large\frac{4}{5}$ = 0.2 × 4 = 0.8

Converting Between More Complex Fractions and Decimals

E.g.1 Fraction to decimal

$\large\frac{71}{100}$ is the same as 0.71.
- $\large\frac{71}{100}$ is the same as 0.71 because there are 7 'tenths' and 1 'hundredth' in 0.71.

E.g.1 Fraction to decimal cont.

0.7 can be shown in two ways.
- There are 7 'tenths' in 0.7 so 0.7 can be shown as $\large\frac{7}{10}$
- 0.7 is also the same as 70 'hundredths' so can be shown as $\large\frac{70}{100}$

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E.g.2 Decimal to fraction

$\large\frac{3}{10}$ is the same as 0.3.
$\large\frac{3}{10}$ can also be shown as $\large\frac{30}{100}$

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E.g.3 Decimal to fraction

0.42 can be shown as $\large\frac{42}{100}$

1Year 5 - Number

1.1Number & Place Value

1.1.1The Value of Digits to Millions

1.1.2Smallest & Biggest Numbers to Millions

1.1.3Ordering Numbers to Millions

1.1.4Counting in Powers of 10

1.1.5Counting in Negative Numbers

1.1.6Rounding Numbers up to 1,000,000

1.1.7Reading Roman Numerals

1.2Addition & Subtraction

1.2.1Written Methods for Adding Large Numbers

1.2.2Written Methods for Subtracting Large Numbers

1.2.3Mental Addition & Subtraction

1.2.4Rounding to Check Your Answer

1.3Multiplication & Division

1.3.1Multiples

1.3.2Factors

1.3.3Prime Numbers

1.3.4Prime Factors

1.3.5Composite Numbers

1.3.6Factor Trees

1.3.7Multiplication by a 1 Digit Number

1.3.8Long Multiplication Using Column Method

1.3.9Times Tables

1.3.10Division

1.3.11Multiplying & Dividing by 10, 100 & 1,000

1.3.12Square & Cube Numbers

1.4Fractions & Decimals

1.4.1Compare & Order Fractions

1.4.2Identifying Equivalent Fractions

1.4.3Add & Subtract Fractions

1.4.4Mixed Numbers & Improper Fractions

1.4.5Multiplying Fractions by Whole Numbers

1.4.6Converting Between Decimals & Fractions

1.4.7Rounding Decimals

1.4.8Ordering Decimals

2Year 5 - Measurement

2.1Measures

2.1.1Metric Measurements

2.1.2Imperial Measurements

2.2Perimeter & Area

2.2.1Perimeter

2.2.2Area

2.3Time

2.3.1Units of Time

3Year 5 - Geometry

3.1Properties of 3D Shapes

3.1.1Types of 3D Shapes

3.1.2Faces, Edges & Vertices

3.2Properties of 2D Shapes

3.2.1Polygons

3.3Angles

3.3.1Angles in Degrees

3.3.2Types of Angle

3.3.3Finding Missing Angles

3.4Position & Direction

3.4.1Reflection & Translation

4Year 5 - Statistics

4.1Graphs

4.1.1Line Graphs

4.1.2Tables

4.1.3Timetables

5Year 6 - Number

5.1Number & Place Value

5.1.1The Value of Digits to Ten Millions

5.1.2Ordering Numbers to Millions

5.1.3Rounding

5.1.4Negative Numbers

5.2Multiplication & Division

5.2.1Multiplication by a 2 Digit Number

5.2.2Division

5.2.3Multiples

5.2.4Factors

5.2.5Primes

5.3Mental Maths

5.3.1Multiplying & Dividing by 10, 100 & 1,000

5.3.2Addition & Subtraction

5.3.3Adding & Subtracting 10, 100 & 1,000

5.3.4Multiplication & Division

5.4Order of Operations

5.4.1BIDMAS

5.5Problem Solving

5.5.1Addition & Subtraction Multi-step Problems

5.5.2Problem Solving with Proportion

5.6Fractions & Decimals

5.6.1Simplifying Fractions Using Equivalents

5.6.2Ordering Different Types of Fraction

5.6.3Adding & Subtracting Fractions

5.6.4Adding & Subtracting Mixed Numbers

5.6.5Multiplying Fractions

5.6.6Dividing Fractions by Whole Numbers

5.6.7Converting Between Decimals & Fractions

5.6.8Dividing Decimals

6Year 6 - Ratio & Proportion

6.1Ratio

6.1.1Using Ratios

6.1.2Simplifying Ratios

6.2Percentages

6.2.1Calculating Percentages

6.3Scale

6.3.1Scale of 2D Shapes

7Year 6 - Algebra

7.1Sequences

7.1.1Describing Sequences

7.1.2Finding Gaps in Sequences

7.2Missing Number Problems

7.2.1Missing Number Problems

7.3Equations

7.3.1Balancing Equations

7.3.2Combining Two Variables

8Year 6 - Measurement

8.1Problem Solving

8.1.1Problem Solving with Measures

8.2Unit Conversion

8.2.1Conversion Between Miles & Kilometres

8.3Perimeter, Area & Volume

8.3.1Area

8.3.2Volume

8.3.3Nets

8.3.4Faces, Edges & Vertices

8.4Angles

8.4.1Types of Angle

8.4.2Finding Missing Angles

8.4.3Finding Missing Angles in Triangles

8.4.4Vertically Opposite Angles

8.5Circles

8.5.1Parts of a Circle

8.6Coordinate Grids

8.6.1Positions on Coordinate Grids

8.6.2Reflection & Translation

9Year 6 - Statistics

9.1Displaying Data

9.1.1Pie Charts

9.1.2Line Graphs

9.2Averages

9.2.1Mean

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