A topographical map has a statement scale of 1\text{ cm to } 2.5\text{ km}. What is the Re… — JAMB UTME

A topographical map has a statement scale of $1\text{ cm to } 2.5\text{ km}$ . What is the Representative Fraction (RF) of this map?

1 : 250,000

To convert a statement scale of

1\text{ cm to } 2.5\text{ km}

to a Representative Fraction (RF), both measurements must be brought to the same unit (centimeters). Since

1\text{ km} = 100,000\text{ cm}

, multiplying

2.5\text{ km}

100,000

yields

250,000\text{ cm}

. Therefore,

1\text{ cm}

on the map represents

250,000\text{ cm}

on the ground, giving an RF of

1 : 250,000

Identify the given statement scale

The statement scale is

1\text{ cm to } 2.5\text{ km}

Converting to a Representative Fraction requires expressing both map distance and ground distance in identical units.

Convert ground distance from kilometers to centimeters

2.5\text{ km} = 2.5 \times 100,000\text{ cm} = 250,000\text{ cm}

There are

100,000\text{ cm}

1\text{ km}

(

1,000\text{ m} \times 100\text{ cm/m}

Formulate the Representative Fraction

The ratio is

\frac{1\text{ cm}}{250,000\text{ cm}} = 1 : 250,000

Representative Fraction is expressed as a ratio

1 : n

without unit labels.

Statement Scale to Representative Fraction Conversion

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