Are the fractions equal?
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Are the fractions equal?
To determine if these two decimal fractions are equal, we compare the numbers directly. The first number is , which is equivalent to the fraction . The second number is , which is equivalent to the fraction .
First, let's convert to thousandths to compare it directly with :
Now, compare and : clearly, .
Therefore, , making the expression false.
Are they the same numbers?
\( 0.23\stackrel{?}{=}0.32 \)
The position of digits matters! means 45 hundredths, while means 45 thousandths. That's like comparing 45 cents to 4.5 cents!
Add zeros to make them the same length: . Now compare digit by digit: 0.450 vs 0.045. Clearly 450 thousandths is much larger than 45 thousandths!
Look at the first non-zero digit after the decimal point. In 0.45, it's in the tenths place (4). In 0.045, it's in the hundredths place (4). The tenths place is always larger!
Absolutely! and . Since , you can clearly see 450 > 45.
Yes! More decimal places usually mean smaller numbers (when the leading digits are the same). 0.045 has 3 decimal places vs 0.45 with 2, so 0.045 is the smaller number.
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