Converting scales

Statement of scale into R.F.: write both sides in the same unit, then drop the unit name and write 1 : N.

• The book's example: 1 inch represents 4 miles = 1 inch represents 4 × 63,360 inches = 253,440 inches, so R.F. = 1 : 253,440.

R.F. into statement of scale: read the R.F. as 1 cm (or 1 inch) to N cm (or inches), then divide the denominator by the number of those small units in the larger unit you want.

• Into kilometres: divide by 1,00,000 (cm in a km). The book turns 1 : 253,440 into 1 cm represents 2.5344 km, about 2.53 km.
• Into metres: divide by 100.
• Into miles: divide by 63,360 (inches in a mile).
• Into furlongs: divide by 7,920 (inches in a furlong: 220 × 36). So 1 : 31,680 means 1 inch represents 4 furlongs.
• Into yards: divide by 36 (inches in a yard).

From the video: the teacher warns that most mistakes in these sums are unit-conversion mistakes, not reasoning mistakes, so learn the conversion table well; a plain R.F.-to-statement conversion is a common multiple-choice question.

Example (new): convert '1 cm represents 250 m' into an R.F. 250 m = 250 × 100 = 25,000 cm, so the R.F. is 1 : 25,000. Going back the other way, 1 : 25,000 ÷ 100 = 250, so 1 cm represents 250 m.