Choose the appropriate sign:
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Choose the appropriate sign:
First, let's convert 0.7 to a simple fraction.
Since there is only one digit after the decimal point, the number divides by 10 as follows:
Now we have two simple fractions with different denominators.
In order to compare them, note that the smallest common denominator between them is 90.
We'll multiply each one to reach the common denominator as follows:
Now we can compare the two fractions and see that:
Are they the same numbers?
\( 0.23\stackrel{?}{=}0.32 \)
Because and have different denominators! Think of it like comparing 6 slices of a 9-piece pizza vs 7 slices of a 10-piece pizza - the pieces are different sizes.
Yes! You can convert both to decimals instead. and , so 0.667 < 0.700.
For denominators 9 and 10, list their multiples:
Remember: the inequality sign always points to the smaller number. Since is smaller than , we write .
It's helpful but not required! when simplified, but you can compare either way. Sometimes it's easier to work with the original fractions.
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