Write each decimal as a fraction or mi 27. 8. 7. 0.675
The Correct Answer and Explanation is :
1. Decimal: 27
- The number 27 is already a whole number, and any whole number can be expressed as a fraction by placing it over 1.
- Fraction:
[
27 = \frac{27}{1}
]
2. Decimal: 8
- Similarly to the previous example, 8 is a whole number and can be written as a fraction by placing it over 1.
- Fraction:
[
8 = \frac{8}{1}
]
3. Decimal: 7
- Like the others, 7 is also a whole number and can be expressed as a fraction.
- Fraction:
[
7 = \frac{7}{1}
]
4. Decimal: 0.675
- To convert a decimal like 0.675 into a fraction, follow these steps:
- Count the number of decimal places. In this case, there are three decimal places (thousandths).
- Remove the decimal by multiplying both the numerator and denominator by 1,000 (since it’s in the thousandths place).
- This gives:
[
0.675 = \frac{675}{1000}
] - Now, simplify the fraction by finding the greatest common divisor (GCD) of 675 and 1000. The GCD of 675 and 1000 is 25.
- Divide both the numerator and denominator by 25:
[
\frac{675}{1000} = \frac{675 \div 25}{1000 \div 25} = \frac{27}{40}
]
- Fraction:
[
0.675 = \frac{27}{40}
]
Explanation of Conversion Process:
When converting decimals to fractions, the key is to recognize the place value of the decimal. For whole numbers like 27, 8, and 7, they are already integers and don’t need conversion. For decimals like 0.675, the number of decimal places determines the denominator of the fraction. By shifting the decimal to the right, we convert the decimal to an integer, and then simplify the resulting fraction by finding the GCD of the numerator and denominator. This ensures the fraction is in its simplest form.