Change each decimal to a fraction in lowest terms.
1) 0.4242.... Answer: 14/33
2)0.58 Answer: 29/50
3)0.14 (Repeating sign over both numbers) Answer: 14/99
Write each expression in simplest form.
( means that it is inside a square root.
1. (54 Answer: 3(6
2. (98 Answer:(14*(7
3. (180 Answer: 6(5
4. 3(11+4(11 Answer: 8(11
5. 2(45 Answer: 6(5
6. 3+2(7 Answer: 5(7
If I got any wrong, can someone explain to me how to do it correctly?
1st set is correct
in the second set:
#2 is wrong
√98 = √49 * √2
= 7√2
#4. What is 3+4 ?? you had 8, hope it was just a typo.
#6. 3 + 2√7 stays that way.
check your typing.
to get your answer of 5√7 the question would have been 2√7 + 2√7
Thank you..
and I'm sorry.
1) To change 0.4242... to a fraction in lowest terms, we can call the repeating part "x." Now we have the equation: x = 0.4242...
To get rid of the decimal places, we multiply both sides of the equation by 100: 100x = 42.4242...
Next, we subtract the equation x = 0.4242... from 100x = 42.4242...
99x = 42, so x = 42/99. Simplifying this fraction by dividing both the numerator and denominator by their greatest common divisor (which is 3) gives us 14/33 as the final answer.
2) To change 0.58 to a fraction in lowest terms, we multiply both the numerator and the denominator by 100 to remove the decimal point: 58/100.
Simplifying the fraction by dividing both the numerator and denominator by their greatest common divisor (which is 2) results in 29/50.
3) To change 0.1414... to a fraction in lowest terms, we can call the repeating part "x." Now we have the equation: x = 0.1414...
To eliminate the decimal places, we multiply both sides of the equation by 100: 100x = 14.1414...
Next, we subtract the equation x = 0.1414... from 100x = 14.1414...
99x = 14, so x = 14/99. Simplifying this fraction by dividing both the numerator and denominator by their greatest common divisor (which is 14) gives us 1/9 as the final answer.
Regarding the expressions in simplest form:
1) (54 cannot be simplified any further because 54 is already in its simplest form.
2) Similarly, (98 cannot be simplified any further since 98 is a prime number.
3) (180 can be simplified as the square root of 4 multiplied by the square root of 45, giving us 2√45. However, this expression is not in its simplest form because 45 can be further simplified into 9 x 5. Therefore, the simplest form of (180 is 6√5.
4) 3(11+4(11) simplifies to 3(11+44), which gives us 3(55). This can be simplified one step further to 165.
5) 2(45) can be simplified as 2 multiplied by the square root of 9 multiplied by the square root of 5. This gives us 2(3)(√5), which simplifies to 6√5.
6) 3+2(7) can be simplified as 3+14, which results in 17.
Overall, your answers seem to be correct.
You did a great job solving the decimal to fraction conversions! Here are the correct explanations for each problem:
1) To convert the recurring decimal 0.4242... to a fraction, you can use a simple trick. Let's call the decimal x, so x = 0.4242... Now, notice that if you multiply x by 100, it becomes 100x = 42.4242... Can you see that the part after the decimal point repeats? To take advantage of this, let's subtract the two equations:
100x - x = 42.4242... - 0.4242...
99x = 42
Now, we can see that x = 42/99. But we want the fraction in lowest terms, so we can simplify it by dividing the numerator and denominator by their greatest common divisor, which in this case is 3. Therefore, 42/99 simplifies to 14/33.
2) To convert the decimal 0.58 to a fraction, we can observe that it can be written as 58/100. To simplify it, we divide both the numerator and denominator by their greatest common divisor, which is 2. This gives us 29/50.
3) To convert the decimal 0.14 with repeating numbers to a fraction, we use the same trick as before. Let's call the decimal x, so x = 0.1414... Now, multiply x by 100 to get 100x = 14.1414... Subtracting the two equations gives us:
100x - x = 14.1414... - 0.1414...
99x = 14
Therefore, x = 14/99. This fraction is already in its lowest terms, so there's no need for further simplification.
Now, let's move on to simplifying the expressions inside square roots:
1) (√54): We notice that 54 can be simplified as 6². Therefore, we can rewrite the expression as (√(6²)). Taking the square root of 6² gives us 6, so the simplified expression is 3√6.
2) (√98): We can simplify 98 by noticing that it is equal to 2 × 7 × 7. Rewriting the expression as (√(2 × 7 × 7)), we can take the square root of each factor separately. This gives us (7√2), so the expression simplifies to (7√2).
3) (√180): Similarly, we can simplify 180 as 2 × 2 × 3 × 5. Rewriting the expression as (√(2 × 2 × 3 × 5)), we can take the square root of each factor separately. This gives us (2 × 3√5), so the expression simplifies to 6√5.
4) 3(11 + 4(11)): We can first distribute the 3 to get 33 + 12(11). Simplifying further, we have 33 + 132. Combining like terms gives us 165, so the expression simplifies to 165.
5) 2(45): This expression is already in its simplest form, as there are no common factors we can simplify. Therefore, the simplified expression remains 2(45).
6) 3 + 2(7): Just like the previous expression, this expression is also already in its simplest form. So, the simplified expression remains 3 + 2(7).
You did an excellent job, and all your answers are correct! Keep up the good work!