| Percent - a special form of fraction | Percent Models | Ratios | | Relationships:decimal fractions, common fractions, percent and also ratio | prices | rapid quiz |

Percent - a special type of fraction

0.25, 1/4, 25%

These expressions tell united state what section of the square is coloured orange.

You are watching: What is 0.25% of 25?

The word percent come indigenous the expression "per cent" and also literally method "a component of one hundred". A percent is a part, or fraction, out of 100. For example:

100% | =100/100 | =1 | = 1.0 (decimal) | |

50% | = 50/100 | = 5/10 | = 1/2 | = 0.5 = 0.50 (decimal) |

25% | = 25/100 | = 5/20 | = 1/4 | = 0.25 (decimal) |

40% | = 40/100 | = 4/10 | = 2/5 | = 0.4 (decimal) |

5% | = 5/100 | = 1/20 | = 0.05 (decimal) | |

0.5% | = 5/1000 | = 1/200 | = 0.005 (decimal) |

We can see the to write a percent together a portion we to express the percent as a fraction with a denominator the 100. We may then be able to simplify the fraction further.

For example, 75% = 75/100 = 3/4

To to express a fraction as a percent us must very first convert the fraction into hundredths (in an easy cases we can do this through using tantamount fractions) and then change "/100" through the percent "%" sign.

For example, 4/5 = 80/100 = 80%

We can see that us express a percent together a decimal by splitting by 100.

For example,

25% = 25/100 = 0.25 (twenty-five hundredths) |

47.3 % = 47.3/100 = 0.473 (forty 7 hundredths and 3 thousandths) |

200% = 200/100 = 2 |

To refer a decimal together a percent we multiply the decimal number by 100.

For example,

0.108 = 0.108 x 100 = 10.8% |

0.75 = .75 x 100 = 75% |

1.2 = 1.2 x 100 = 120% |

**Some percents expressed together fractions and decimals**

| = 0.125 (decimal) | |

= 0.236 (decimal) | ||

= 0.333 (decimal, rounded to 3 decimal places) | ||

= 0.5 = 0.50 (decimal) | ||

= 0.667 (decimal, rounded come 3 decimal places) | ||

= 1.1 (decimal) | ||

= 1.5 (decimal) | ||

=2.0 (decimal) |

Example 1: 30 the end of 50 apologize in a box are too bruised to sell. What percent of apples cannot be sold?

Working Out | Thinking |

30 out of 50 apples are bruised. To represent 30/50 together a percent we need to uncover out how plenty of apples the end of 100 room bruised. By indistinguishable fractions we understand that 30 the end of 50 equates to 60 out of 100, for this reason 60% the the apples space bruised. us could additionally say that, 3/5 of the apples are bruised 0.6 of the apples are bruised. |

Example 2: Ryan invested 25 minute in the bank, 11 minute of i beg your pardon was invested waiting in a queue. What percent that time go he spend waiting in the queue?

Working Out | Thinking |

Ryan invested 11 minutes the end of 25 minutes wait in a queue. To turn this right into a percent we room asking, 11 the end of 25 minutes amounts to how many minutes out of 100 minutes? We deserve to see the 11 mins the end of 25 mins amounts to 44 mins the end of 100 mins by identical fractions (because we know 25 x 4 = 100) . We can say that Ryan invested 44%, 0.44 or 11/25 that his time in the financial institution waiting in a queue. |

Example 3: What percent is 7 centimeter of 20 cm?

Working Out | Thinking |

To find out what percent 7 the end of 20 is, we have to ask: 7 out of 20 is how plenty of out the 100? 5 groups of 20 do 100, for this reason 7 out of 20 is 35 out of 100 (5 x 7 out of 5 x 20). Therefore 7/20 equates to 35%, or 0.35 if we stand for it together a decimal. |

Percent models

**Dual-scale number line model**

We deserve to use the dual-scale number line, also called the proportional number line, to illustrate instance 1 from above.

Recall example 1: 30 the end of 50 apologize in a box space too bruised come sell. What percent the apples can not be sold? | |

Thinking | |

The left side of the number line below has a percent scale. The right side of the number line has actually a number scale. We have the right to label each scale using the details we are offered in the problem. | We understand that there are 50 apples in total, ie. 50 apples amounts to 100% the the apples. We know that 30 out of the 50 apples room bruised and we need to uncover what percent this is. In more facility problems this dual-scale number line is a great way the organising the information we room given and to work out what info we must find. Once we have represented the trouble in this way we have the right to write a ratio equation straight from the number line. 30/50 = ?/100 By indistinguishable fractions we know that 30/50 = 60/100. (Or we can have simply noticed the it is a "multiply by 2" relationship, for this reason 30 x 2 = 60) Therefore 60% of apples are too bruised to sell. |

The dual-scale number line model is debated further in the other pages of the Percent, Ratio and also Rates topic.

**Elastic tape measure up model**

The tape measure model is a good linear model of percent. Teacher can easily make this models using a ruler, such as a 1 metre ruler, and elastic. The elastic needs to be marked with a percent scale. It deserve to then be stretched to the preferred length.

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For example, what is 60% that 50?

To find the answer us line up the zeros of the ruler and the elastic. Us then big the elastic so the 100% lines up with the whole amount, i beg your pardon in this instance is 50. We then look for 60% ~ above the elastic and also read the corresponding amount top top the ruler. We can see listed below that 60% that 50 is 30.

The intention is no to usage this design accurately. It is a an excellent way of mirroring that percent constantly involves a proportional to compare of something come 100.

1 metre ruler Elastic |

By manipulating the ice cream measure, this model deserve to be provided for the 3 types of percent problems, discussed in Percent Examples. Examples of i beg your pardon are,

What is 20% of 50?** What percent is 10 of 50? 30% of what number is 15?**

(Note: because that a lesson, a teacher will require elastics tape steps of assorted lengths, due to the fact that the elastic have the right to only be extended - it cannot be shrunk).