Question

comparing decimals

1. which of the following comparisons is not true? circle the letter of the correct answer.

a. 42.300 = 42.3
b. 5.020 = 5.02
c. 0.149 < 1.490
d. 108.308 > 108.4
ana chose a as the correct answer. how did she get that answer?

1. elle fills her car with 14.291 gallons of gas. alivia fills her car with 14.209 gallons of gas. write an inequality statement comparing the two gas - purchases. show your work.
2. heathers rabbit has a mass of 5,190 kilograms. jeffs rabbit has a mass of 5,195 kilograms. write an inequality statement comparing the masses of the rabbits.
3. brayden and his cousin kayla live twenty miles away from each other. on the same day, brayden recorded 1.046 inches of rain at his house and kayla recorded 1.062 inches of rain at her house. whose house received fewer inches of rain that day?

Explanation:

Step1: Analyze option A

$42.300$ has trailing zeros after the decimal - point. In decimal numbers, trailing zeros after the last non - zero digit after the decimal do not change the value. So $42.300 = 42.3$.

Step2: Analyze option B

$5.020$ has a non - zero digit ($2$) between the decimal point and the trailing zero. So $5.020
eq5.20$.

Step3: Analyze option C

$0.149$ is less than $1.498$ as the whole - number part of $0.149$ is $0$ and the whole - number part of $1.498$ is $1$. So $0.149<1.498$.

Step4: Analyze option D

$108.308$ has a value greater than $108$ since it has a non - zero value after the decimal point. So $108.308 > 108$.

Step1: Compare the two gas amounts

Ella fills her car with $14.291$ gallons and Alivia fills her car with $14.209$ gallons.
We start comparing from the left - most digit after the decimal point. The tenths place is the same ($2$ for both). Then we compare the hundredths place. $9>0$.

Step2: Write the inequality

Since $14.291$ is greater than $14.209$, the inequality is $14.291>14.209$.

Step1: Compare the two masses

Heather's rabbit has a mass of $5.190$ kilograms and Jeff's rabbit has a mass of $5.195$ kilograms.
The whole - number part and the tenths and hundredths places are the same for both numbers. We compare the thousandths place. $0 < 5$.

Step2: Write the inequality

Since $5.190$ is less than $5.195$, the inequality is $5.190<5.195$.

Step1: Compare the two rain amounts

Brayden recorded $1.046$ inches of rain and Kayla recorded $1.062$ inches of rain.
The whole - number part and the tenths place are the same for both numbers. We compare the hundredths place. $4<6$.

Step2: Determine who received less rain

Since $1.046$ is less than $1.062$, Brayden's house received fewer inches of rain.

Answer:

B. $5.020 = 5.20$ is not true.

For the gas - purchase inequality: