Write 7/40 as a decimal. Use bar notation if necessary
The Correct Answer and Explanation is :
To convert the fraction ( \frac{7}{40} ) into a decimal, we can use long division or a calculator. Here’s a step-by-step explanation of the process:
Step 1: Division Setup
We need to divide 7 by 40. In long division, we set it up as follows:
- 40 goes into 7, which cannot happen since 40 is greater than 7.
- Therefore, we extend the division by adding decimal places. We rewrite 7 as 7.000 and proceed with the division.
Step 2: Long Division Process
- 40 into 70: 40 goes into 70 once. This gives us 1, and we write down 1 after the decimal point.
- Subtract ( 40 \times 1 = 40 ) from 70, leaving us with ( 70 – 40 = 30 ).
- Bring down the next 0: We bring down the next 0, making it 300.
- 40 into 300: 40 goes into 300 seven times since ( 40 \times 7 = 280 ).
- Subtract ( 280 ) from ( 300 ), which leaves us with ( 300 – 280 = 20 ).
- Bring down the next 0: We bring down another 0, making it 200.
- 40 into 200: 40 goes into 200 five times since ( 40 \times 5 = 200 ).
- Subtract ( 200 ) from ( 200 ), which leaves us with ( 200 – 200 = 0 ).
At this point, the division ends because there is no remainder.
Step 3: Result
The decimal representation of ( \frac{7}{40} ) is ( 0.175 ).
Conclusion
In summary, ( \frac{7}{40} ) converts to the decimal ( 0.175 ). There are no repeating decimals or further complexities in this case. The fraction represented a division where we added decimal places and found the quotient through a series of divisions, ultimately leading us to a finite decimal. This method is particularly useful for converting fractions to decimals, especially when the denominator is not a factor of 10, leading to non-terminating decimals in other scenarios.