Find practice problems and solutions for these concepts at Dealing with Decimals Practice Problems.

### What's Around The Bend

- What Is a Decimal?
- Padding a Decimal with Zeros
- Moving the Decimal Point to the Right and to the Left
- Arranging Decimals in Order
- Adding and Subtracting Decimals
- Rewriting a Decimal
- Multiplying Decimals
- Dividing Decimals

**Decimals are really** just fractions in disguise. Or maybe it's the fractions that are really decimals in disguise. You may never know who's disguised as what in this crazy world of mathematical espionage. One thing is for sure: You can equate fractions and decimals. For example, the fraction can be written as the decimal 0.1.

A decimal carries the decimal place-value system, which is based on the number 10, into the domain of fractions that are based on 10, namely , , , etc.

To review the place-value system briefly, a whole number (e.g., 234) is the sum of its digits, each one multiplied, respectively, by 100, 10, and 1:

234 = (2 × 100) + (3 × 10) + (4 × 1) = 200 + 30 + 4

A decimal expands on this concept, bringing in fractions as multipliers. The number 234.567 is equal to the sum of its digits, 2, 3, 4, 5, 6, and 7, each one multiplied, respectively, by 100, 10, 1, , , and :

234.567 = (2 × 100) + (3 × 10) + (4 × 1) + (5 × ) + (6 × ) + (7 × ) = 200 + 30 + 4 + 0.5 + 0.06 + 0.007

In the following table, the places to the right of the decimal point are named for the number 0.987654321.

## Fuel for Thought## The Invisible Decimal PointProfessor: Is there a lamp on this table?Student: Yes.Professor: Is it on?Student: No.Professor (turning the lamp on): Is it on now?Student: Yes.Now they look at a whole number, 23.Professor: Does 23 have a decimal point?Student: Yes.Professor: Is it turned on? In other words, can you see it?Student: No.Professor: Now look at this number: 23.0. Does it have a decimal point?Student: Yes.Professor: Is it turned on?Student: Yes.Professor: Like the lamp, the decimal point in a whole number is always there, whether it is turned on or not. |

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