GCSE(F),

It is often necessary to switch between different standard units: for example, moving from centimetres to metres. The table below shows the relationship between standard units.

When calculating larger changes: for example, changing kilometres to centimetres, it is often easier to carry out the calculation in two steps and using an intermediate value. For kilometres to centimetres, change the kilometres to metres, then change the metres to centimetres.

measure | ||||
---|---|---|---|---|

time | 60 seconds in a minute | 60 minutes in an hour | 24 hours in a day | |

calendar | 7 days in a week | see below for days in a month | 12 months in a year | see below for days in a year |

length | 10mm in a centimetre (cm) | 100cm in a metre (m) | 1000m in a kilometre (km) | |

area | 100mm^{2} in a square centimetre | 10 000cm^{2} in a square metre | 1 000 000m^{2} in a square kilometre | |

volume | 1 000mm^{3} in 1cm^{3} | 1 000 000cm^{3} in a cubic metre | ||

capacity | 1000ml in a litre | |||

mass | 1000g in a kilogram (kg) | 1000kg in a tonne |

Special notes on the calendar: in a Leap Year (2016, 2020, 2024, 2028), the year is 366 days long and February has 29 days. All other years are 365 days long and February is 28 days long. April, June, September and November are each 30 days long: the remaining months are each 31 days long.

1. How many centimetres are in 4.25km?

Answer: 425,000

Change 4.25km to metres by multiplying by 1000 (1000m in a km) = 4.25 x 1000 = 4250m.

Change 4250m to cm by multiplying by 100 (100cm in a m) = 4250 x 100 = 425 000cm.

2. How many complete hours are there in 1 000 000 seconds?

Answer: 277 days

Divide 1 000 000 by 60 to get minutes (60 minutes in an hour) = 16.66666 minutes.

Divide 16.6666 by 60 to get hours (60 minutes in an hour) = 277.777 hours.

The question asked for complete hours, so 277 hours.

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