NCERT Revision Notes for Class 5 Maths Chapter 5: Far and Near – Free PDF Download

Chapter 5 of Class 5 Maths, Far and Near, focuses on measuring and comparing distances – understanding standard units of length (millimetres, centimetres, metres, kilometres), converting between them, and estimating and comparing distances between near and far places using maps and everyday travel.

Key Concepts

Units of Length

Length is measured using a chain of standard units: 10 millimetres (mm) = 1 centimetre (cm); 100 cm = 1 metre (m); 1,000 m = 1 kilometre (km). Small, nearby lengths (a pencil, a notebook) are measured in cm or mm; larger, far-off distances (between cities, along a road) are measured in km.

Converting Between Units

To convert a bigger unit to a smaller one, multiply (1 km = 1,000 m, so 3 km = 3,000 m). To convert a smaller unit to a bigger one, divide (2,500 m = 2,500 ÷ 1,000 = 2.5 km). Keeping the conversion factor (1,000, 100, or 10) in mind is the key to moving between units correctly.

Estimating Distance

Before measuring exactly, it helps to estimate – comparing an unknown distance to a known one (“the market is about as far as my school”) builds a practical sense of near and far that is useful even without tools.

Reading Distances on a Map

Maps often show distance using a scale, where a small measured length on the paper represents a much larger real distance on the ground. Reading the scale correctly lets us estimate real-world distances between two points marked on a map.

Comparing Distances (Near and Far)

Comparing two distances means converting them to the same unit first, then comparing the numbers directly – for example, to compare 2.5 km and 2,300 m, convert 2.5 km to 2,500 m, then compare 2,500 m with 2,300 m (2,500 m is farther).

Decimal Notation for Distance

Distances that are not a whole number of kilometres are often written using decimals, such as 3.2 km (which means 3 km and 200 m, since 0.2 km = 200 m).

Worked Examples

Example 1: Converting km to m

Convert 4.5 km to metres.
4.5 × 1,000 = 4,500 m.

Example 2: Converting m to km

Convert 6,750 m to km.
6,750 ÷ 1,000 = 6.75 km.

Example 3: Comparing Two Distances

Which is farther: 1.8 km or 1,750 m?
Convert 1.8 km to metres: 1.8 × 1,000 = 1,800 m. Compare 1,800 m and 1,750 m – 1,800 m is farther, so 1.8 km is the greater distance.

Quick Recap

• Length units chain together: 10 mm = 1 cm, 100 cm = 1 m, 1,000 m = 1 km.
• Convert bigger to smaller units by multiplying; smaller to bigger by dividing.
• Estimating distance by comparing to a known, familiar distance is a useful practical skill.
• Map scales let us translate a short measured length on paper into a real, larger distance.
• Always convert to the same unit before comparing two distances.

Common Mistakes to Avoid

• Multiplying instead of dividing (or vice versa) when converting between units – always check whether the target unit is bigger or smaller.
• Misreading a decimal distance, such as thinking 3.2 km means 3 km 2 m instead of the correct 3 km 200 m.
• Comparing two distances written in different units without converting them first.
• Forgetting the map scale entirely and guessing real distances just from how far apart two points look on paper.
• Using the wrong unit for the size of object or distance being measured (using km for a pencil, or mm for a road trip).

Home Practice Tips

• Use a ruler or measuring tape to measure small objects at home in cm and mm, then convert the measurements to metres.
• Check the distance to a few nearby landmarks (school, market, park) using a map app, and practise converting the shown distance between km and m.
• Estimate the distance between two rooms in the house by pacing it out, then measure and compare with the estimate.
• Practise writing a few distances as decimals, like “2 km 400 m” as “2.4 km,” and back again.
• Look at a road atlas or map with a printed scale and estimate the real distance between two marked towns.

Frequently Asked Questions

Q1. Why do we use different units for different distances?
Because using kilometres for a pencil’s length or millimetres for the distance between cities would give impractically large or tiny numbers – choosing an appropriately sized unit keeps measurements easy to read and use.

Q2. How do I remember whether to multiply or divide when converting units?
If you are changing from a bigger unit to a smaller one (like km to m), the number of units increases, so multiply; if changing from a smaller to a bigger unit (like m to km), the number decreases, so divide.

Q3. What does a map scale actually tell us?
It tells us how a small distance measured on the map corresponds to a real distance on the ground, such as “1 cm on the map represents 1 km in real life.”

Q4. Why is 3.2 km equal to 3 km 200 m and not 3 km 2 m?
Because the digits after the decimal point in “3.2 km” represent tenths of a kilometre, and 0.2 km = 0.2 × 1,000 m = 200 m, not 2 m.

Q5. Is estimating distance a useful skill even with GPS and maps available?
Yes – being able to judge roughly how far something is builds practical number sense and helps sanity-check whether a calculated or map-read distance seems reasonable.

Full walkthrough: Chapter 5 Solutions · Extra Questions.

Written by Satish

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