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Door 9 · Grade 4

🔢 Decimals (Tenths and Hundredths)

Tenths: first place after decimal point, denominator 10

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Fractions as Decimals

A decimal is another way to write a fraction. A decimal point separates the whole number part from the fractional part.
• Tenths place: first digit after decimal = denominator 10 (e.g. 3/10 = 0.3)
• Hundredths place: second digit after decimal = denominator 100 (e.g. 25/100 = 0.25)

Think of it like Indian currency: Rs.1 = 100 paise. 10 paise = 10/100 = 0.10. 1 paisa = 1/100 = 0.01.
Converting fractions to decimals: Make the denominator 10 or 100, then write in decimal form. Adding a zero to the right of a decimal does NOT change its value: 0.3 = 0.30.

Worked example

Problem: Write 7/10 as a decimal.

  1. Denominator is 10, so we need 1 digit after decimal point.
  2. Numerator is 7.
  3. Write as 0.7.
  4. Check: 0.7 means 7 tenths = 7/10.

Answer: Check: 0.7 means 7 tenths = 7/10.

Compare Decimals

Comparing decimals: line up the decimal points and compare digit by digit from left to right.
Steps:
• Line up the decimal points (add zeros if needed)
• Compare the ones place first
• If same, compare tenths
• If same, compare hundredths
• The first place where digits differ decides which is larger

Important: 0.3 = 0.30 (adding a zero on the right does not change the value, it just allows comparison).

Worked example

Problem: Compare 0.6 and 0.59.

  1. Write 0.6 as 0.60.
  2. Compare tenths: 6 vs 5.
  3. 6 > 5, so 0.6 > 0.59.

Answer: 6 > 5, so 0.6 > 0.59.

Add and Subtract Decimals

The most important rule for adding/subtracting decimals: ALWAYS line up the decimal points!
Column Method Steps:
• Write numbers with decimal points aligned
• Add zeros to make same number of decimal places
• Add or subtract from RIGHT to LEFT (like whole numbers)
• Bring the decimal point STRAIGHT DOWN into the answer
• Carry or borrow just like with whole numbers

Worked example

Problem: Add 4.25 + 0.75.

  1. Line up decimals: 4.25 + 0.75.
  2. Hundredths: 5+5=10 (write 0, carry 1).
  3. Tenths: 2+7+1=10 (write 0, carry 1).
  4. Ones: 4+0+1=5.

Answer: 5.00 = 5.