Find a rational number between 2 and 2/14 using the method of adding the numbers together and dividing by 2. Write the answer as a mixed number.(1 point)
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To find a rational number between 2 and 2/14 using the method of adding the numbers together and dividing by 2, we can follow these steps:
1. Convert 2/14 to a decimal by dividing 2 by 14: 2 ÷ 14 = 0.142857...
2. Add 2 and the decimal: 2 + 0.142857... = 2.142857...
3. Divide the sum by 2: 2.142857... ÷ 2 = 1.0714285...
4. Write the result as a mixed number. Since the decimal part is recurring, we can round it to the nearest rational number: 1.0714285... ≈ 1Ⅿ⋅¹⁰⁸⁵⁷
Therefore, the rational number between 2 and 2/14 is approximately 1Ⅿ⋅¹⁰⁸⁵⁷.
2.142857 as a mixed number
To express 2.142857 as a mixed number, we can follow these steps:
1. Identify the whole number part: The whole number part of 2.142857 is 2.
2. Calculate the fractional part: Subtract the whole number part from the original number: 2.142857 - 2 = 0.142857.
3. Express the fractional part as a fraction. Since the decimal part has six digits after the decimal point (142857), it can be written as a fraction with that number as the numerator and a denominator of 999999 (or any multiple of 9 repeated the same number of times):
0.142857 = 142857/999999.
4. Simplify the fraction if possible. In this case, the fraction cannot be further simplified.
5. Put the whole number, the fraction, and the fractional part together to form the mixed number:
2 + 142857/999999 = 2 142857/999999.
Therefore, 2.142857 can be expressed as the mixed number 2 142857/999999.
2.14 as a mixed number
To express 2.14 as a mixed number, follow these steps:
1. Identify the whole number part: The whole number part of 2.14 is 2.
2. Calculate the fractional part: Subtract the whole number part from the original number: 2.14 - 2 = 0.14.
3. Express the fractional part as a fraction. Since there are two digits after the decimal point, we can write it as 14/100.
4. Simplify the fraction if possible. In this case, we can simplify 14/100 by dividing both numerator and denominator by their greatest common divisor, which is 2:
14/100 = (14 ÷ 2) / (100 ÷ 2) = 7/50.
5. Put the whole number, the fraction, and the fractional part together to form the mixed number:
2 + 7/50 = 2 7/50.
Therefore, 2.14 can be expressed as the mixed number 2 7/50.
Find a rational number between 2 and 2 1/4 using the method of adding the numbers together and dividing by 2. Write the answer as a mixed number
To find a rational number between 2 and 2 1/4 using the method of adding the numbers together and dividing by 2, we can follow these steps:
1. Convert 2 1/4 to an improper fraction: 2 1/4 = (2 * 4 + 1) / 4 = 9/4.
2. Add 2 and 9/4: 2 + 9/4 = 8/4 + 9/4 = 17/4.
3. Divide the sum by 2: (17/4) ÷ 2 = 17/4 ÷ 2 = 17/4 * 1/2 = 17/8.
4. Write the result as a mixed number:
- Divide the numerator by the denominator to find the whole number part: 17 ÷ 8 = 2 remainder 1.
- The whole number part is 2.
- Write the fraction part as the numerator over the denominator: 1/8.
- Put the whole number and the fraction together to form the mixed number:
2 1/8.
Therefore, a rational number between 2 and 2 1/4 using the given method is 2 1/8.
Find a rational number with one decimal place that is between 17−−√ and 18−−√.(1 point)
To find a rational number with one decimal place between √17 and √18, we can follow these steps:
1. Approximate the values of √17 and √18:
- √17 ≈ 4.123105625617661
- √18 ≈ 4.242640687119286
2. Find the midpoint between these two approximations by adding them together and dividing by 2:
- (4.123105625617661 + 4.242640687119286) / 2 ≈ 4.182873156368473
3. Round the midpoint to one decimal place:
- Rounded to one decimal place, the rational number between √17 and √18 is approximately 4.2.
Therefore, a rational number with one decimal place that is between √17 and √18 is 4.2.