Lesson 2: Reading, Writing, and Modeling Decimals

Property

To name a decimal number:

1. Name the number to the left of the decimal point (the whole number).
2. Write 'and' for the decimal point.
3. Name the number to the right of the decimal point as if it were a whole number.
4. Name the decimal place of the last digit. The 'th' at the end of the name means the number is a fraction.

Examples

• The number 0.4 is read as 'four tenths' because the 4 is in the tenths place.
• The number 0.62 is read as 'sixty-two hundredths' because the 2 is in the hundredths place.
• The number 0.05 is read as 'five hundredths' because the 5 is in the hundredths place.
• The number 0.7 is read as 'seven tenths' because the 7 is in the tenths place.

Explanation

Naming decimals is like telling a number's full story. The part before 'and' is the whole number, and the part after is the fraction. The last word, like 'hundredths', tells you the size of the fractional pieces.

Property

Decimals can be written as fractions with denominators of 10 or 100. This connection explains why different representations can describe the same value, even though they look different.

• Tenths (one decimal place): $0.a = \frac{a}{10}$
• Hundredths (two decimal places): $0.ab = \frac{ab}{100}$

Examples

• 0.6 is the same as $\frac{6}{10}$.
• 0.4 is the same as $\frac{4}{10}$.
• 0.30 is the same as $\frac{30}{100}$.
• 0.75 is the same as $\frac{75}{100}$.

Explanation

Decimals are another way to write fractions that have denominators of 10 and 100. The number of digits to the right of the decimal point tells you which denominator to use. One decimal place means the denominator is 10 (tenths), and two decimal places means the denominator is 100 (hundredths). The number itself becomes the numerator of the fraction.