Decimals

Lesson

A benchmark is a reference point against which we can compare or make judgements about numbers. There are a few common fractions and decimals (and percentages) that we use as benchmarks.

The pictures below show these benchmark fractions:

$0.1$0.1 | $0.2$0.2 | $0.25$0.25 | $0.5$0.5 | $0.75$0.75 |

$10$10 out of $100$100 |
$20$20 out of $100$100 |
$25$25 out of $100$100 |
$50$50 out of $100$100 |
$75$75 out of $100$100 |

In the first grid block, $10$10 out of $100$100 squares are shaded. We could also simplify this and say $1$1 out of the $10$10 columns are shaded, which, if you remember looking at the place value table, is written as $0.1$0.1 as a decimal.

So what about when we see a decimal like $0.5$0.5 written?

Well, just think $0.5$0.5 means $5$5 tenths or $\frac{5}{10}$510 (or $\frac{50}{100}$50100 like is shown in the grid block above), which we can simplify to $\frac{1}{2}$12.

Here's a table that summarises these benchmark fractions, decimals and percentages.

Decimal | Fraction | Fraction in lowest terms | Percentage |
---|---|---|---|

$0.1$0.1 | $\frac{10}{100}$10100 | $\frac{1}{10}$110 | $10%$10% |

$0.2$0.2 | $\frac{20}{100}$20100 | $\frac{1}{5}$15 | $20%$20% |

$0.25$0.25 | $\frac{25}{100}$25100 | $\frac{1}{4}$14 | $25%$25% |

$0.5$0.5 | $\frac{50}{100}$50100 | $\frac{1}{2}$12 | $50%$50% |

$0.75$0.75 | $\frac{75}{100}$75100 | $\frac{3}{4}$34 | $75%$75% |

Write the decimal $0.75$0.75 as a simplified fraction.

Convert $6.125$6.125 into an improper fraction or mixed number. Give your answer in simplest form.

Write the decimal $3.8$3.8 as a mixed or improper fraction, giving your answer as a simplified fraction.

Determine and explain, through investigation using concrete materials, drawings, and calculators, the relationship between fractions (i.e.,with denominators of 2, 4, 5, 10, 20, 25, 50, and 100) and their equivalent decimal forms (e.g., use a 10 x 10 grid to show that 2/5 = 40/100, which can also be represented as 0.4)