Olympiad Notes: Conversions | Math Olympiad for Class 5 PDF Download

Introduction

Imagine following a recipe that uses cups, but your measuring tool shows grams, or travelling to another country and needing to convert your currency. Conversions help us compare, measure, and calculate across different units and formats. In this chapter, we’ll explore three main types of conversions: 

• Units of Measurement
• Money
• Fractions

Converting Units of Measurement

We measure things using units for length, weight, volume, and time.Sometimes, we need to convert one unit to another to make it easier to compare values. Let’s explore these with examples.

Length Conversion

• 1 kilometer (km) = 1,000 meters (m)
• 1 meter (m) = 100 centimeters (cm)
• 1 foot (ft) = 12 inches (in)
• 1 mile = 1,609 meters

Conversion from Kilometers to Meters

Example: Ravi walks 2.5 kilometres every morning. How many meters does he walk?
Ans:Ravi walks 2,500 meters every morning.

Explanation:
We know that 1 kilometer is equal to 1,000 meters.
To convert kilometers to meters, we multiply the number of kilometers by 1,000.

Calculation:
2.5km×1,000=2,500m

Conversion from Centimeters to Meters

Example:A pencil measures 18 centimeters. What is its length in meters?
Ans: The pencil is 0.18 meters long.

Explanation:
We know that 1 meter is equal to 100 centimeters.
To convert centimeters to meters, we divide the number of centimeters by 100.
Calculation:
18cm÷100=0.18m

Weight Conversion

• 1 kilogram (kg) = 1,000 grams (g)
• 1 pound (lb) = 16 ounces (oz)

Conversion from Kilograms to Grams

Example: A bag of sugar weighs 4.5 kilograms. How many grams is that?
Ans: The bag weighs 4,500 grams.

Explanation:
We know that 1 kilogram is equal to 1,000 grams.
To convert kilograms to grams, we multiply the number of kilograms by 1,000.

Calculation:

4.5kg×1,000=4,500g

Example: Riya’s cat weighs 8 pounds. How many ounces is that?
Ans:The cat weighs 128 ounces.

Explanation:
We know that1 pound is equal to 16 ounces.
To convert pounds to ounces, we multiply the number of pounds by 16.

Calculation:
8lb×16=128oz

Time Conversion

• 1 hour = 60 minutes
• 1 minute = 60 seconds
• 1 day = 24 hours

Conversion from Hours and Minutes to Minutes

Example: A movie lasts 2 hours and 15 minutes. How many minutes is that?
Ans: The movie is 135 minutes long.

Explanation:
We know that 1 hour is equal to 60 minutes.
To convert hours and minutes into just minutes, we first multiply the number of hours by 60 and then add the remaining minutes.

Calculation:
(2hours × 60) + 15minutes = 135minutes

Conversion from Seconds to Minutes

Example: If you exercise for 540 seconds, how many minutes is that?
Ans: Your workout lasts 9 minutes.

Explanation:
We know that 1 minute is equal to 60 seconds.
To convert seconds to minutes, we divide the number of seconds by 60.

Calculation:
540seconds÷60=9minutes

Converting Money

Currency conversion helps us when we travel or shop internationally.Let’s learn how to convert between currencies and smaller denominations.

Currency Conversion Using Exchange Rates

Currencies have different values, and exchange rates show how much one currency is worth compared to another.

Conversion from USD to INR

Example 1: If 1 USD = 83 INR, how many rupees will you get for 50 USD?
Ans: 50 USD equals 4,150 INR.

Explanation:
To convert USD to INR, multiply the number of USD by the conversion rate (1 USD = 83 INR).
Calculation:
50USD×83INR=4,150INR

Conversion from INR to GBP

Example: Lina visits the UK with 2,000 INR. If 1 GBP = 100 INR, how many pounds will she get?
Ans: Lina will get 20 GBP.

Explanation:
To convert INR to GBP, divide the number of INR by the conversion rate (1 GBP = 100 INR).
Calculation:
2,000INR÷100INR/GBP=20GBP

Converting Coins and Notes

In many currencies, smaller units combine to make larger ones (like 100 paise = 1 rupee).

Conversion from Paise to Rupees

Example: You have 275 paise. How many rupees is that?
Ans: 275 paise equals 2.75 rupees.

Explanation:
We know that 1 rupee equals 100 paise.
To convert paise to rupees, divide the number of paise by 100.

Calculation:
275paise÷100=2.75rupees

Conversion from Cents to Dollars

Example: A toy costs 350 cents. How many dollars is that?
Ans: The toy costs 3.5 dollars.

Explanation:

We know that 1 dollar equals 100 cents.

To convert cents to dollars, divide the number of cents by 100.

Calculation:

350cents÷100=3.5dollars

Converting Fractions

Fractions represent parts of a whole. We often convert them to decimals, percentages, or mixed numbers.

Fraction to Decimal Conversion

To convert a fraction to a decimal, divide the numerator by the denominator.

Conversion from Fraction to Decimal

Example 1: Convert 1/5  to a decimal.

Ans: 1/5 equals 0.2.

Explanation:

To convert a fraction to a decimal, divide the numerator by the denominator.

Calculation:

1/5 =1÷5=0.2

Example 2: Convert 7/8  to a decimal.
Ans: 7/8 equals 0.875.

Explanation:

To convert a fraction to a decimal, divide the numerator by the denominator.

Calculation:

7/8 =7÷8=0.875

Fraction to Percentage Conversion

To convert a fraction to a percentage, multiply it by 100 and add the % symbol.

Conversion from Fraction to Percentage

Example 1: Convert 3/5  to a percentage.
Ans: 
3/5  equals 60%.

Explanation:

To convert a fraction to a percentage, multiply the fraction by 100.

Calculation:

3/5×100=60%

Example 2: Convert 2/3  to a percentage.
Ans: 2/3 equals 66.67%.

Explanation:

To convert a fraction to a percentage, multiply the fraction by 100.

Calculation:

2/3×100=66.67%

Improper Fraction to Mixed Number Conversion

Improper fractions have numerators larger than denominators. To convert them into mixed numbers, divide the numerator by the denominator.

Conversion from Improper Fraction to Mixed Number

Example 1: Convert 9/4to a mixed number.
Ans: 9/4 is 2 whole and 1/4.

Explanation:

To convert an improper fraction to a mixed number, divide the numerator by the denominator. The quotient becomes the whole number, and the remainder over the original denominator becomes the fractional part.

Calculation:
9/4=2 whole 1/4

Example 2: Convert 11/3 to a mixed number.
Ans:  11/33 is 3 whole and 2/3.

Explanation:
To convert an improper fraction to a mixed number, divide the numerator by the denominator. The quotient is the whole number, and the remainder over the original denominator becomes the fractional part.

Calculation:
11/3=3 whole2/3

Solved Examples

1. Unit Conversion:
   Convert 6.8 kilometers to meters.
   6.8 km×1,000=6,800 m

2. Currency Conversion:
   If 1 EUR = 90 INR, how much is 30 EUR in INR?
   30×90=2,700 INR

3. Fraction to Decimal:
   Convert 5/8 to a decimal.
   5÷8=0.625

4. Mixed Number Conversion:
   Convert 13/5 into a mixed number.
   13/5=2 whole 3/5

Conclusion

Conversions are essential foreveryday tasks—whether you’re measuring ingredients, traveling abroad, or solving math problems. Understanding how to switch between units, currencies, and fractions makes life easier. With practice, these conversions will become second nature and a valuable skill in everyday life!