To write the decimal number 2.034 in expanded form, we need to break it down into its constituent parts and express each part as a fraction. Here’s a step-by-step explanation on how to do that:
1. Identify the whole number part of the decimal. In this case, the whole number is 2.
2. Determine the tenths place. In 2.034, the digit in the tenths place is 0. This means there are zero tenths.
3. Determine the hundredths place. In 2.034, the digit in the hundredths place is 3. This means there are three hundredths.
4. Determine the thousandths place. In 2.034, the digit in the thousandths place is 4. This means there are four thousandths.
Now, let's express each part separately:
- The whole number part is 2.
- The tenths part can be written as [tex]\( \frac{0}{10} \)[/tex].
- The hundredths part can be written as [tex]\( \frac{3}{100} \)[/tex].
- The thousandths part can be written as [tex]\( \frac{4}{1000} \)[/tex].
Combining all these parts, we get the expanded form of the decimal number:
[tex]\[ 2 + \frac{0}{10} + \frac{3}{100} + \frac{4}{1000} \][/tex]
Therefore, the decimal number 2.034 written in expanded form is:
[tex]\[ 2 + \frac{0}{10} + \frac{3}{100} + \frac{4}{1000} \][/tex]
