## Naming Decimals

You probably already know quite a bit about decimals based on your experience with money. Suppose you buy a sandwich and a bottle of water for lunch. If the sandwich costs \(\text{\$3.45}\), the bottle of water costs \(\text{\$1.25}\), and the total sales tax is \(\text{\$0.33}\), what is the total cost of your lunch?

The total is \(\text{\$5.03}.\) Suppose you pay with a \(\text{\$5}\) bill and \(3\) pennies. Should you wait for change? No, \(\text{\$5}\) and \(3\) pennies is the same as \(\text{\$5.03}.\)

Because \(\text{100 pennies}=\text{\$1},\) each penny is worth \(\frac{1}{100}\) of a dollar. We write the value of one penny as \(\$0.01,\) since \(0.01=\frac{1}{100}.\)

Writing a number with a decimal is known as decimal notation. It is a way of showing parts of a whole when the whole is a power of ten. In other words, decimals are another way of writing fractions whose denominators are powers of ten. Just as the counting numbers are based on powers of ten, decimals are based on powers of ten. The table below shows the counting numbers.

Counting number | Name |
---|---|

\(1\) | One |

\(10=10\) | Ten |

\(10·10=100\) | One hundred |

\(10·10·10=1000\) | One thousand |

\(10·10·10·10=10,000\) | Ten thousand |

How are decimals related to fractions? The table below shows the relation.

Decimal | Fraction | Name |
---|---|---|

\(0.1\) | \(\frac{1}{10}\) | One tenth |

\(0.01\) | \(\frac{1}{100}\) | One hundredth |

\(0.001\) | \(\frac{1}{1,000}\) | One thousandth |

\(0.0001\) | \(\frac{1}{10,000}\) | One ten-thousandth |

When we name a whole number, the name corresponds to the place value based on the powers of ten. In Mathematics 101, we learned to read \(10,000\) as *ten thousand*. Likewise, the names of the decimal places correspond to their **fraction** values. Notice how the place value names in the figure below relate to the names of the fractions from the table above

Notice two important facts shown in the figure above.

- The “th” at the end of the name means the number is a fraction. “One thousand” is a number larger than one, but “one thousandth” is a number smaller than one.
- The tenths place is the first place to the right of the decimal, but the tens place is two places to the left of the decimal.

Remember that \(\text{\$5}.03\) lunch? We read \(\text{\$5.03}\) as *five dollars and three cents*. Naming decimals (those that don’t represent money) is done in a similar way. We read the number \(5.03\) as *five and three hundredths*.

We sometimes need to translate a number written in **decimal notation** into words. As shown in the figure below, we write the amount on a check in both words and numbers.

Let’s try naming a decimal, such as 15.68. | |

We start by naming the number to the left of the decimal. | fifteen______ |

We use the word “and” to indicate the decimal point. | fifteen and_____ |

Then we name the number to the right of the decimal point as if it were a whole number. | fifteen and sixty-eight_____ |

Last, name the decimal place of the last digit. | fifteen and sixty-eight hundredths |

The number \(15.68\) is read *fifteen and sixty-eight hundredths*.

### How to Name a decimal number.

- Name the number to the left of the decimal point.
- Write “and” for the decimal point.
- Name the “number” part to the right of the decimal point as if it were a whole number.
- Name the decimal place of the last digit.

## Example

Name each decimal:

- \(\phantom{\rule{0.2em}{0ex}}4.3\)
- \(\phantom{\rule{0.2em}{0ex}}2.45\)
- \(\phantom{\rule{0.2em}{0ex}}0.009\)
- \(\phantom{\rule{0.2em}{0ex}}-15.571.\)

### Solution

4.3 | |

Name the number to the left of the decimal point. | four_____ |

Write “and” for the decimal point. | four and_____ |

Name the number to the right of the decimal point as if it were a whole number. | four and three_____ |

Name the decimal place of the last digit. | four and three tenths |

2.45 | |

Name the number to the left of the decimal point. | two_____ |

Write “and” for the decimal point. | two and_____ |

Name the number to the right of the decimal point as if it were a whole number. | two and forty-five_____ |

Name the decimal place of the last digit. | two and forty-five hundredths |

0.009 | |

Name the number to the left of the decimal point. | Zero is the number to the left of the decimal; it is not included in the name. |

Name the number to the right of the decimal point as if it were a whole number. | nine_____ |

Name the decimal place of the last digit. | nine thousandths |

\(-15.571\) | |

Name the number to the left of the decimal point. | negative fifteen |

Write “and” for the decimal point. | negative fifteen and_____ |

Name the number to the right of the decimal point as if it were a whole number. | negative fifteen and five hundred seventy-one_____ |

Name the decimal place of the last digit. | negative fifteen and five hundred seventy-one thousandths |