Convert the following statement scales to RF scale: i) 2cm to 1km, ii) 1cm to 1km

March 16, 2026Mathematics

ScanSolve AI Answer

March 16, 2026

Answer

1:200000

Step 1: Convert the ground distance of 2 km to cm, keeping units consistent.

Formula:
$1~km = 1000~\mathrm{m}$
$1~m = 100~\mathrm{cm}$
$1~km = 1000 \times 100 = 100{,}000~\mathrm{cm}$

Substitute for 2 km:
$2~km = 2 \times 100{,}000~cm = 200{,}000~\mathrm{cm}$

Step 2: Form the representative fraction (RF) scale using same units (cm) for map and ground distances.

Map distance = $1~\mathrm{cm}$
Ground distance = $200{,}000~\mathrm{cm}$

RF scale:
$1~cm : 200{,}000~cm = 1 : 200{,}000$

Final answer:
1:200000

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Quick Answer

Convert the ground distance of 2 km to cm, keeping units consistent.

Asked on March 16, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI AnswerAnswered on March 16, 2026

Step 1: Convert the ground distance of 2 km to cm, keeping units consistent. Formula: 1~km = 1000~m 1~m = 100~cm 1~km = 1000 × 100 = 100,000~cm Substitute for 2 km: 2~km = 2 × 100,000~cm = 200,000~cm Step 2: Form the representative fraction (RF) scale using same units (cm) for map and ground distances. Map distance = 1~cm Ground distance = 200,000~cm RF scale: 1~cm : 200,000~cm = 1 : 200,000 Final answer: 1:200000