1. Definition of Decimal Numbers

• A decimal number is a number that consists of a whole number part and a fractional part, separated by a decimal point.
  Example: 7.45 (7 is the whole number, 45 is the fractional part).

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2. Place Value in Decimal Numbers

• Place values extend both to the left and right of the decimal point:
  • Left: Ones, Tens, Hundreds, etc.
  • Right: Tenths, Hundredths, Thousandths, etc.
  • Example: In 45.678,
    • 4 is in the Tens place.
    • 5 is in the Ones place.
    • 6 is in the Tenths place.
    • 7 is in the Hundredths place.
    • 8 is in the Thousandths place.

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3. Converting Fractions to Decimals

• Divide the numerator by the denominator.

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4. Converting Decimals to Fractions

• Write the decimal as a fraction with a denominator based on place value and simplify.

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5. Adding and Subtracting Decimals

• Align the decimal points.
• Add or subtract as usual.
• Place the decimal point directly below in the result.
  Example:
  3.42+5.6=9.02.

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6. Multiplying Decimals

• Multiply the numbers ignoring the decimal point.
• Count the total decimal places in both numbers.
• Place the decimal in the product.
  Example:
  3.2×1.5=4.80.

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7. Dividing Decimals

• Move the decimal point in the divisor to make it a whole number.
• Move the decimal in the dividend the same number of places.
• Divide as usual and place the decimal point in the quotient.
  Example:
  4.2÷0.7=6.

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8. Comparing and Ordering Decimals

• Compare digits starting from the leftmost place value.
• Add trailing zeroes to equalize the number of decimal places if needed.
  Example: 0.25<0.3.

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9. Rounding Decimals

• Identify the rounding place.
• Look at the digit to the right:
  • If ≥5, round up.
  • If <5, round down.
    Example: Round 3.276 to two decimal places → 3.28.

Learn with an example

Try some practice problems!