We want to order the numbers from least to greatest.
- 3/4, 0.5, 2/3 , - 7/3 , 1.2
To help us compare the numbers, we will first rewrite the fractions - 34, 23, and - 73 as decimals.
Rewrite - 34 as a Decimal
We want to write the fraction - 34 as a decimal number. Let's ignore the negative sign for the moment. Since 3 4 means 3÷ 4, we will divide the numerator by the denominator. Let's do it!
We found that 3 4 written as a decimal is 0.75. This means that - 34 written as a decimal is - 0.75.
Rewrite 23 as a Decimal
Now let's write the fraction 23 as a decimal number by dividing the numerator by the denominator.
We can see that the pattern starts to repeat itself after a few steps. This means that the decimal is a repeating decimal, so let's write it using bar notation. Remember, the bar goes over the decimal part that repeats itself.
0.666... = 0.6
We found that 23 written as a decimal is 0.6.
Rewrite - 73 as a Decimal
We want to write the fraction - 73 as a decimal number. We will ignore the negative sign for now. Recall that 7 3 means 7÷ 3, so let's divide the numerator by the denominator.
We can see that the pattern starts to repeat itself after a few steps. This means that the decimal is a repeating decimal. Let's write it in bar notation.
2.333... = 2.3
We found that 7÷ 3 written as a decimal is 2.3, which means that - 73 written as a decimal is - 2.3.
Order the Numbers from Least to Greatest
Let's organize our decimal numbers.
- 3/4, 0.5, 2/3 , - 7/3 , 1.2
⇕
- 0.75, 0.5, 0.6 , - 2.3 , 1.2
Now we can compare the given numbers by plotting the decimals on the number line.
Looking at the diagram, we can see that the least number is - 2.3. We read the numbers from left to right to rearrange them in order from least to greatest.
- 2.3 , - 0.75, 0.5 , 0.6 , 1.2
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⇕
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- 7/3 , - 3/4, 0.5 , 2/3 , 1.2
