Decimal place values

key notes:

1. Understanding Decimal Numbers

• Decimal numbers represent parts of a whole.
• They consist of two parts separated by a decimal point:
  • Whole Number Part (to the left of the decimal point).
  • Fractional Part (to the right of the decimal point).

Example: In 12.345,

• 12 is the whole number.
• 345 is the fractional part.

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2. Decimal Place Value Chart

Example: 1234.567

• 1 is in the thousands place.
• 2 is in the hundreds place.
• 3 is in the tens place.
• 4 is in the ones place.
• 5 is in the tenths place.
• 6 is in the hundredths place.
• 7 is in the thousandths place.

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3. Value of Decimal Places

• Tenths: The first place after the decimal point (1/10).
  • Example: 0.3 = 3 tenths = 3/10.
• Hundredths: The second place after the decimal point (1/100).
  • Example: 0.03 = 3 hundredths = 3/100.
• Thousandths: The third place after the decimal point (1/1000).
  • Example: 0.003 = 3 thousandths = 3/1000.

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4. Reading Decimal Numbers

• Read the whole number part first, then the decimal part by its place value.
  • Example: 45.67 is read as “forty-five and sixty-seven hundredths.”

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5. Writing Decimals in Expanded Form

• Break down the number into its place values.
  • Example: 23.456 = 20 + 3 + 0.4 + 0.05 + 0.006.

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6. Comparing Decimals

• Compare digits from left to right, starting with the whole number.
• If the whole numbers are equal, compare the fractional part digit by digit.
  • Example: 0.45 > 0.408 because 5 (tenths) > 4 (hundredths).

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7. Rounding Decimals

• Look at the digit to the right of the place you want to round to:
  • If it’s 5 or greater, round up.
  • If it’s less than 5, round down.
  • Example: Round 12.456 to the nearest hundredth → 12.46.

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8. Real-Life Applications

• Money: $12.34 (12 dollars and 34 cents).
• Measurements: 2.75 meters (2 meters and 75 centimeters).
• Scientific Data: 3.142 (approximating π).

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9. Practice Questions

1. Write 45.678 in expanded form.
2. Compare: 0.56 and 0.569.
3. Round 13.456 to the nearest tenth.
4. Identify the place value of 7 in 56.078.

Learn with an example

let’s practice :