Question

solve the expression. use pemdas 2.1+(9.2×3.3)×0.8= solve the following problem. 2.004×10³= order the numbers from least to greatest. 44.22 44.20 44.02 44

Explanation:

First Problem: Solve \([2.1+(9.2 \times 3.3)] \times 0.8\) using PEMDAS

Step1: Solve inside the parentheses (multiplication)

First, we calculate the multiplication inside the innermost parentheses: \(9.2 \times 3.3\).
\(9.2\times3.3 = 30.36\)

Step2: Solve inside the brackets (addition)

Next, we add \(2.1\) to the result from Step 1 inside the brackets: \(2.1 + 30.36\).
\(2.1+30.36 = 32.46\)

Step3: Multiply by 0.8

Finally, we multiply the result from Step 2 by \(0.8\): \(32.46\times0.8\).
\(32.46\times0.8 = 25.968\)

Step1: Understand \(10^{3}\)

Recall that \(10^{3}=10\times10\times10 = 1000\).

Step2: Multiply by 2.004

Now, multiply \(2.004\) by \(1000\). When multiplying a decimal by \(1000\), we move the decimal point three places to the right.
\(2.004\times1000 = 2004\)

Step1: Compare the whole number part

All numbers have a whole number part of \(44\), so we move to the decimal part.

Step2: Compare the tenths place

• \(44\) can be written as \(44.00\). The tenths place of \(44.00\) is \(0\), the tenths place of \(44.02\) is \(0\), the tenths place of \(44.20\) is \(2\), and the tenths place of \(44.22\) is \(2\).

Step3: Compare the hundredths place (for numbers with the same tenths place)

• For \(44.00\) and \(44.02\): The hundredths place of \(44.00\) is \(0\) and the hundredths place of \(44.02\) is \(2\). So \(44.00<44.02\).
• For \(44.20\) and \(44.22\): The hundredths place of \(44.20\) is \(0\) and the hundredths place of \(44.22\) is \(2\). So \(44.20<44.22\).

Step4: Order all numbers

Putting it all together, we have \(44<44.02<44.20<44.22\).

Answer:

\(25.968\)

Second Problem: Solve \(2.004 \times 10^{3}\)