Understanding Decimals
Decimals are a way to represent fractional numbers using the base 10 system. They use a period (.) to separate the whole number part from the fractional part. For example, the decimal 0.5 represents the fraction 1/2.
1/7 as a Decimal
To convert 1/7 to a decimal, we can use long division:
7 ) 1.000
- 7
___
03
- 2
___
10
- 7
___
30
- 28
___
20
- 14
___
60
- 56
___
40
- 42
___
18
As we can see, the long division process continues indefinitely, with no remainder ever reaching 0. This indicates that 1/7 is a non-terminating, repeating decimal. The decimal representation of 1/7 is:
1/7 = 0.142857142857...
The repeating block of digits is 142857.
Tips and Tricks
Common Mistakes to Avoid
Why 1/7 as a Decimal Matters
Converting 1/7 to a decimal is important for several reasons:
Benefits of Using Decimals
There are several benefits to using decimals:
Comparison of Pros and Cons
Characteristic | Pros | Cons |
---|---|---|
Ease of use | Easier to understand and calculate | Can be more difficult to convert to and from fractions |
Precision | Can represent fractions with greater precision | Can be more difficult to read and compare |
Application | Used in a wide variety of applications, including calculations, measurement, and money | Not as commonly used as fractions in some contexts |
Tables
Table 1: Common Decimals
Decimal | Fraction |
---|---|
0.5 | 1/2 |
0.25 | 1/4 |
0.75 | 3/4 |
0.125 | 1/8 |
0.375 | 3/8 |
Table 2: Conversions from 1/n to Decimals
Fraction | Decimal |
---|---|
1/2 | 0.5 |
1/3 | 0.333... |
1/4 | 0.25 |
1/5 | 0.2 |
1/6 | 0.166... |
1/7 | 0.142857... |
1/8 | 0.125 |
Table 3: Examples of Decimal Use
Application | Example |
---|---|
Calculations | 0.5 x 2 = 1 |
Measurement | A ruler measuring 12.5 centimeters |
Money | A cost of $14.99 |
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