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U.1 Identify decimal numbers using visual models

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What is a decimal?

Decimals are numbers that show parts of a whole. A decimal point separates the whole number part from the fractional part.

Example:
  • 3.7 means 3 wholes and 7 tenths.
  • 0.25 means 25 hundredths, or 25 out of 100.
Note

The decimal point is always read as “and” when reading a number aloud. For example, 4.56 is read as “four and fifty-six hundredths.”

Understanding decimal place value

Each digit in a decimal number has a value based on its place. The places to the right of the decimal point represent tenths, hundredths, thousandths, and so on.

Example:
  • In 6.482, the 4 is in the tenths place, the 8 is in the hundredths place, and the 2 is in the thousandths place.
Note

Each place to the right of the decimal point is ten times smaller than the one before it. For example, tenths are ten times larger than hundredths.

How to identify decimal place values

To find the place value of a digit in a decimal, locate its position to the right or left of the decimal point and name the place accordingly.

Steps:
  • Find the decimal point.
  • Count the places to the right to identify tenths, hundredths, thousandths, etc.
  • Say the digit’s value using its place name.
Example:
  • In 9.307, the 3 is in the tenths place, the 0 is in the hundredths place, and the 7 is in the thousandths place.
Note

You can use a place value chart to help organize digits by their place. This makes comparing decimals easier.

Comparing and ordering decimals

To compare decimals, line up the decimal points and compare digits from left to right. The first different digit determines which number is greater.

Examples:
  • 0.56 < 0.7 because 0.56 has 5 tenths while 0.7 has 7 tenths.
  • 1.305 > 1.25 because 3 tenths is greater than 2 tenths.
Note

Always compare digits in the same place value. You can add zeros to the end of a decimal to make comparison easier (for example, 0.5 = 0.50).

Reading and writing decimals

When reading decimals, say the whole number first, then say “and,” followed by the fractional part with its place name. When writing, use digits and a decimal point.

Examples:
  • Read 2.4 as “two and four tenths.”
  • Read 5.08 as “five and eight hundredths.”
  • Read 0.625 as “six hundred twenty-five thousandths.”
Note

Do not say “point” when reading the number in word form. Always name the place value of the last digit instead.