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question 79
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which number has the greater value?
select one:
a. $2\frac{3}{10}$
b. 2.03
question 80
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which number has the greater value?
select one:
a. $\frac{7}{14}$
b. $\frac{1}{3}$
question 81
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round to the nearest thousandth if necessary
$3.75 \div 0.25$
answer:

Explanation:

Question 79

Step1: Convert mixed number to decimal

The mixed number \( 2\frac{3}{10} \) can be converted to a decimal. The fraction part \( \frac{3}{10} = 0.3 \), so \( 2\frac{3}{10}=2 + 0.3=2.3 \).

Step2: Compare decimals

Now we compare \( 2.3 \) (from option a) and \( 2.03 \) (from option b). Since \( 2.3>2.03 \), the number in option a has a greater value.

Step1: Simplify fraction a

Simplify \( \frac{7}{14} \). We can divide both the numerator and the denominator by 7, so \( \frac{7\div7}{14\div7}=\frac{1}{2} = 0.5 \).

Step2: Convert fraction b to decimal

Convert \( \frac{1}{3} \) to a decimal. \( \frac{1}{3}\approx0.333\cdots \)

Step3: Compare decimals

Now we compare \( 0.5 \) (from option a) and \( 0.333\cdots \) (from option b). Since \( 0.5 > 0.333\cdots \), the number in option a has a greater value.

Step1: Perform the division

We need to calculate \( 3.75\div0.25 \). We can multiply both the numerator and the denominator by 100 to eliminate the decimals, so \( \frac{3.75\times100}{0.25\times100}=\frac{375}{25} \).

Step2: Divide the integers

Now divide 375 by 25. \( 375\div25 = 15 \). Since 15 is an integer, we don't need to round to the nearest thousandth.

Answer:

a. \( 2\frac{3}{10} \)

Question 80