Let's convert the given fractions into decimals step by step.
### Converting Fractions to Decimals
#### Fraction 1: [tex]\(\frac{22}{100}\)[/tex]
1. The fraction [tex]\(\frac{22}{100}\)[/tex] can be interpreted as dividing 22 by 100.
2. To convert this to a decimal, we can move the decimal point in 22 two places to the left (because 100 has two zeros).
So, [tex]\(\frac{22}{100}\)[/tex] equals:
[tex]\[ 0.22 \][/tex]
#### Fraction 2: [tex]\(\frac{22}{1,000}\)[/tex]
1. The fraction [tex]\(\frac{22}{1,000}\)[/tex] can be interpreted as dividing 22 by 1,000.
2. To convert this to a decimal, we move the decimal point in 22 three places to the left (because 1,000 has three zeros).
So, [tex]\(\frac{22}{1,000}\)[/tex] equals:
[tex]\[ 0.022 \][/tex]
### Relationship Between the Digit '2' in Each Decimal
Now, let’s examine the place values of the digit '2' in each decimal.
#### Decimal 1: [tex]\(0.22\)[/tex]
- The decimal [tex]\(0.22\)[/tex] has two digits '2'.
- The first '2' is in the tenths place.
- The second '2' is in the hundredths place.
#### Decimal 2: [tex]\(0.022\)[/tex]
- The decimal [tex]\(0.022\)[/tex] also has two digits '2'.
- The first '2' is in the hundredths place.
- The second '2' is in the thousandths place.
#### Relationship of Place Values
- In [tex]\(0.22\)[/tex], the digit '2' appears in the tenths and hundredths places.
- In [tex]\(0.022\)[/tex], the digit '2' appears in the hundredths and thousandths places.
The place value of the digit '2' in [tex]\(0.022\)[/tex] (hundredths place) is one-tenth of its place value in [tex]\(0.22\)[/tex] (tenths place). Similarly, the place value of the digit '2' in the thousandths place (in [tex]\(0.022\)[/tex]) is one-tenth of its place value in the hundredths place (in [tex]\(0.22\)[/tex]).
Or more specifically:
- The digit '2' in [tex]\(0.022\)[/tex] (hundredths place) corresponds to a value of [tex]\(\frac{2}{100} = 0.02\)[/tex].
- The digit '2' in [tex]\(0.22\)[/tex] (tenths place) corresponds to a value of [tex]\(\frac{2}{10} = 0.2\)[/tex].
Therefore, the digit '2' in the second decimal ([tex]\(0.022\)[/tex]) has a place value that is one-tenth (0.1) of the place value of '2' in the first decimal ([tex]\(0.22\)[/tex]).
