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).

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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Converting Fractions to Decimals

Divide the numerator by the denominator.

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Converting Decimals to Fractions

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

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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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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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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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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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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!