Question

1. convert $1\frac{4}{9}$ to a decimal. round to the hundredths place if necessary.

\bigcirc 1.45
\bigcirc 1.49
\bigcirc 1.44
\bigcirc 1.99

Explanation:

Step1: Convert fraction to decimal

First, we handle the fractional part \(\frac{4}{9}\). Divide 4 by 9: \(4\div9 = 0.444\cdots\) (the 4 repeats infinitely).

Step2: Add the whole number

The mixed number is \(1\frac{4}{9}\), so we add the whole number 1 to the decimal we just found: \(1 + 0.444\cdots= 1.444\cdots\)

Step3: Round to hundredths place

To round \(1.444\cdots\) to the hundredths place, we look at the thousandths place, which is 4. Since 4 is less than 5, we round down. So \(1.444\cdots\approx1.44\) when rounded to the hundredths place? Wait, no, wait. Wait, \(1\frac{4}{9}=1 + \frac{4}{9}\). Let's recalculate \(\frac{4}{9}\): \(4\div9 = 0.444\cdots\). So \(1.444\cdots\). When rounding to the hundredths place, the digit in the hundredths place is 4, and the next digit (thousandths) is 4, so we keep the hundredths place as 4? Wait, no, wait, maybe I made a mistake. Wait, \(4\div9 = 0.444\cdots\), so \(1\frac{4}{9}=1.444\cdots\). Rounding to the hundredths place: the number is \(1.444\cdots\), so the hundredths digit is 4, the thousandths digit is 4, which is less than 5, so we round to \(1.44\)? But wait, let's check again. Wait, maybe I miscalculated \(\frac{4}{9}\). Wait, \(9\times0.4 = 3.6\), \(4 - 3.6 = 0.4\), so it's \(0.4 + \frac{0.4}{9}=0.4 + 0.044\cdots=0.444\cdots\). So \(1.444\cdots\). So when rounding to the hundredths place, we look at the third decimal place (thousandths), which is 4, so we don't round up the hundredths place. So \(1.44\). Wait, but let's check the options. The options are 1.45, 1.49, 1.44, 1.99. So 1.44 is an option. Wait, but wait, maybe I made a mistake. Wait, \(1\frac{4}{9}\): let's do the division again. 4 divided by 9: 9 goes into 4 zero, add decimal, 9 goes into 40 four times (4*9=36), remainder 4. So it's 0.444..., so 1.444..., which rounds to 1.44 when rounded to the hundredths place (since the thousandths digit is 4, which is less than 5). So the correct answer should be 1.44.

Wait, but let's check again. Wait, maybe I messed up the rounding. Wait, the number is 1.444..., so the first decimal is 4 (tenths), second is 4 (hundredths), third is 4 (thousandths). So when rounding to the hundredths place, we look at the thousandths place (4) to decide. Since 4 < 5, we keep the hundredths place as 4. So 1.44. So the correct option is 1.44.

Answer:

1.44 (the option C, assuming the options are labeled as A. 1.45, B. 1.49, C. 1.44, D. 1.99. But from the given options, the third option is 1.44, so the answer is 1.44 (the option with 1.44).