Tenths and Hundredths: Class 5 Maths Chapter 10 Guide

What is a 'Tenth'?

Imagine you have a long chocolate bar and you share it equally among 10 friends. Each friend gets one part out of the ten parts. That one part is called a 'one-tenth'. We can write this as a fraction: 1/10. There's also a special decimal way to write it: 0.1. The dot is called the decimal point. Think of a ruler. One centimetre is divided into 10 tiny parts called millimetres. So, 1 millimetre is one-tenth of a centimetre. We can say 1 mm = 1/10 cm, or 1 mm = 0.1 cm. The number to the immediate right of the decimal point shows how many 'tenths' we have. So, 0.3 means we have three-tenths (3/10).

What is a 'Hundredth'?

Now, imagine a big square sheet of paper. If you divide it into 100 small, equal squares, each tiny square is 'one-hundredth' of the whole sheet. We write this as a fraction: 1/100. The decimal way to write it is 0.01. The best real-life example is money! We know that 100 paise make 1 Rupee. So, 1 paisa is one-hundredth of a Rupee. We can write 1 paisa as ₹1/100, or in decimal form as ₹0.01. In decimal numbers, the second place to the right of the decimal point is the 'hundredths' place. So, if you have ₹5.75, it means you have 5 whole rupees, 7 tenths of a rupee (70 paise), and 5 hundredths of a rupee (5 paise).

Understanding Decimal Place Value

1. The Decimal Point — The dot (.) is the most important part. It separates the whole numbers on the left from the fractional parts on the right. For example, in 12.34, '12' is the whole number part.
2. The Tenths Place — The first digit to the right of the decimal point is in the tenths place. In 12.34, the '3' is in the tenths place, which means 3/10 or three-tenths.
3. The Hundredths Place — The second digit to the right of the decimal point is in the hundredths place. In 12.34, the '4' is in the hundredths place, which means 4/100 or four-hundredths.
4. Putting It Together — The number 12.34 means 12 whole units, plus 3 tenths, plus 4 hundredths. You can think of it as 12 + 3/10 + 4/100.

Worked Examples: Decimals in Daily Life

• Example 1: Measuring Length
  Problem: A pencil is 8 cm and 5 mm long. Write its length in centimetres using a decimal.
  Solution:
  Step 1: We know that 10 mm = 1 cm. So, 1 mm = 1/10 cm = 0.1 cm.
  Step 2: This means 5 mm = 5/10 cm = 0.5 cm.
  Step 3: The total length is 8 cm plus 0.5 cm.
  Final Answer: The length of the pencil is 8.5 cm.

• Example 2: Using Money
  Problem: Seema has 3 rupees and 25 paise. Write this amount in rupees using a decimal.
  Solution:
  Step 1: We know that 100 paise = ₹1. So, 1 paisa = 1/100 rupee = ₹0.01.
  Step 2: This means 25 paise = 25/100 rupee = ₹0.25.
  Step 3: The total amount is 3 rupees plus 0.25 rupees.
  Final Answer: Seema has ₹3.25.

• Example 3: Converting Fractions
  Problem: Write the fraction 42/100 as a decimal.
  Solution:
  Step 1: The fraction has 100 as its denominator. This means the last digit will be in the hundredths place (two places after the decimal point).
  Step 2: The numerator is 42. We can think of this as 40/100 + 2/100. 40/100 is the same as 4/10.
  Step 3: So we have 4 in the tenths place and 2 in the hundredths place.
  Final Answer: 42/100 = 0.42.

Important Tip for Exams

Remember that adding a zero to the very end of a decimal does NOT change its value! For example, 0.5 is exactly the same as 0.50. Why? 0.5 means 5/10. 0.50 means 50/100. If you simplify the fraction 50/100 (by dividing both top and bottom by 10), you get 5/10! This is a very useful trick when you need to compare decimals like 0.7 and 0.65. You can think of 0.7 as 0.70, and it's easy to see that 70 hundredths is more than 65 hundredths.

Practice Questions with Solutions

• Q: Write the decimal for 'seven and three-tenths'.
  A: Step 1: 'Seven' is the whole number part. It comes before the decimal point.
  Step 2: 'Three-tenths' is the fractional part. 'Tenths' is the first place after the decimal point. So we write '3' in the tenths place.
  Final answer: 7.3

• Q: Convert 65 millimetres into centimetres using a decimal.
  A: Step 1: Remember that 10 mm = 1 cm. So, to convert mm to cm, we divide by 10.
  Step 2: 65 mm = 65/10 cm. This means 6 whole units and 5 tenths.
  Step 3: Writing this as a decimal, the 6 is the whole number and the 5 is in the tenths place.
  Final answer: 6.5 cm

• Q: Arun bought a notebook for ₹12 and 50 paise. Express this cost in rupees as a decimal.
  A: Step 1: The whole number part is the rupees, which is 12.
  Step 2: The fractional part is the paise. 50 paise is 50/100 of a rupee.
  Step 3: As a decimal, 50/100 is written as 0.50. So, we add the whole part and the decimal part: 12 + 0.50.
  Final answer: ₹12.50

• Q: Write the fraction 8/100 as a decimal.
  A: Step 1: The denominator is 100, which means the number must go up to the hundredths place (two digits after the decimal point).
  Step 2: The numerator is 8. Since we need two decimal places, we have 0 in the tenths place and 8 in the hundredths place.
  Final answer: 0.08

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