Rename each repeating decimal as a fractio in lowest terms. Use Let statement, an equation, a proper solution (using Properties of Equality).
1) 0.87
2) 0.5406
3) 0.048
4) 3.274
2.
.5406 = 5406/10000
count the number of zeros in the denominator, and count the number of digits past the decimals, they are the same
5406/10000
= 2703/5000 ---- divided top and bottom by 2 to reduce , 2 being the HCF
do the others the same
careful in #3
3.
3.274 = 3274/1000 ---- again, notice the number of zeros on the bottom match the number of decimals in the original
= .....
Sorry I repeated these question to you because I forgot to add there are repeating numbers or ellipsis.
To convert a repeating decimal to a fraction in lowest terms, we need to follow these steps:
Step 1: Let x be the value of the repeating decimal.
Step 2: Subtract the repeating decimal from x, so that only the repeating part remains.
Step 3: Set up an equation to represent the relationship between the original repeating decimal and the decimal formed by the repeating part.
Step 4: Solve the equation for the repeating part of the decimal.
Step 5: Convert the repeating part to a fraction.
Let's apply these steps to each of the given decimals.
1) Let's start with 0.87.
Step 1: Let x = 0.87.
Step 2: Subtract the non-repeating part, which is 0, from x: x - 0 = 0.87 - 0 = 0.87.
Step 3: Set up the equation: x = 0.87.
Step 4: Solve for x: 100x = 87.
Step 5: Convert x to a fraction: x = 87/100.
Therefore, 0.87 as a fraction in lowest terms is 87/100.
2) Let's move on to 0.5406.
Step 1: Let x = 0.5406.
Step 2: Subtract the non-repeating part, which is 0, from x: x - 0 = 0.5406 - 0 = 0.5406.
Step 3: Set up the equation: x = 0.5406.
Step 4: Solve for x: 10,000x = 5,406.
Step 5: Convert x to a fraction: x = 5,406/10,000.
To simplify this fraction, we divide the numerator and denominator by their greatest common divisor, which is 2: (5,406 ÷ 2) / (10,000 ÷ 2) = 2,703/5,000.
Therefore, 0.5406 as a fraction in lowest terms is 2,703/5,000.
3) Let's proceed with 0.048.
Step 1: Let x = 0.048.
Step 2: Subtract the non-repeating part, which is 0, from x: x - 0 = 0.048 - 0 = 0.048.
Step 3: Set up the equation: x = 0.048.
Step 4: Solve for x: 1000x = 48.
Step 5: Convert x to a fraction: x = 48/1000.
Again, we simplify the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 8: (48 ÷ 8) / (1000 ÷ 8) = 6/125.
Therefore, 0.048 as a fraction in lowest terms is 6/125.
4) Finally, let's work on 3.274.
Step 1: Let x = 3.274.
Step 2: Subtract the non-repeating part, which is 3, from x: x - 3 = 3.274 - 3 = 0.274.
Step 3: Set up the equation: x = 0.274.
Step 4: Solve for x: 1000x = 274.
Step 5: Convert x to a fraction: x = 274/1000.
To simplify this fraction, we divide the numerator and denominator by their greatest common divisor, which is 2: (274 ÷ 2) / (1000 ÷ 2) = 137/500.
Therefore, 3.274 as a fraction in lowest terms is 137/500.
By following these steps with the Let statement, equation, and proper solution, we can convert each repeating decimal to a fraction in lowest terms.