We want to order the numbers from least to greatest. Let's start by looking at the given numbers!
2.1, - 6/10, - 9/4 , - 0.75 , 5/3
Before we compare the numbers, let's rewrite the fractions - 610, - 94, and 53 as decimals, one fraction at a time.
Rewrite - 610 as a Decimal
We want to rewrite the fraction - 610 as a decimal number. Let's ignore the negative sign for just a moment. Recall that 6 10 means 6÷ 10. Let's divide the numerator by the denominator
We found that 610 written as a decimal is 0.6. This means that - 610 written as a decimal is - 0.6.
Rewrite - 94 as a Decimal
We want to rewrite the fraction - 94 as a decimal number. Like before, we will ignore the negative sign for a moment and divide the numerator by the denominator. Let's do it!
We found that 94 written as a decimal is 2.25, so - 94 written as a decimal is - 2.25.
Rewrite 53 as a Decimal
We want to rewrite the fraction 53 as a decimal number. Let's divide the numerator by the denominator.
We can see that the pattern starts to repeat itself after a few steps. The decimal is a repeating decimal, so we can write it using bar notation by drawing a bar over the repeating digits in the decimal.
1.666... = 1.6
We found that 53 written as a decimal is 1.6.
Order the Numbers from Least to Greatest
First, we will rewrite the numbers in their decimal forms.
2.1, - 6/10, - 9/4 , - 0.75 , 5/3
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2.1, - 0.6, - 2.25 , - 0.75 , 1.6
Now we can compare the given numbers. Let's graph each decimal on the number line.
Looking at the diagram, we can see that the least number is equal to - 2.25. We read the numbers from left to right to rearrange them in order from least to greatest.
- 2.25 , - 0.75, - 0.6 , 1.6 , 2.1
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- 9/4 , - 0.75, - 6/10 , 5/3 , 2.1
