What is the missing expression? 1.09 is equal to ____. Choose the two correct answers.
Understand the Problem
The question is asking to find the expressions that are equivalent to 1.09. It provides multiple choices, requiring the identification of two correct answers that represent the same value as 1.09.
Answer
B and E.
Answer for screen readers
The two correct answers are B: $1 + \frac{9}{100}$ and E: $\frac{100}{100} + \frac{9}{100}$.
Steps to Solve
- Decimal to Fraction Conversion
To find equivalent expressions for $1.09$, start by converting $1.09$ into a fraction.
$$ 1.09 = \frac{109}{100} $$
- Evaluating Each Option
Next, evaluate each option to check if they equal $\frac{109}{100}$:
-
A: $1 + \frac{9}{10}$
Convert $1$ into a fraction.
$$ 1 + \frac{9}{10} = \frac{10}{10} + \frac{9}{10} = \frac{19}{10} $$ -
B: $1 + \frac{9}{100}$
Convert $1$ into a fraction.
$$ 1 + \frac{9}{100} = \frac{100}{100} + \frac{9}{100} = \frac{109}{100} $$ -
C: $\frac{1}{10} + \frac{9}{100}$
Find a common denominator.
$$ \frac{1}{10} = \frac{10}{100} $$ $$ \frac{10}{100} + \frac{9}{100} = \frac{19}{100} $$ -
D: $\frac{10}{100} + \frac{9}{100}$
Add the fractions:
$$ \frac{10}{100} + \frac{9}{100} = \frac{19}{100} $$ -
E: $\frac{100}{100} + \frac{9}{100}$
Add the fractions:
$$ \frac{100}{100} + \frac{9}{100} = \frac{109}{100} $$
- Identifying Correct Options
The correct expressions equal to $1.09$ are those evaluated to $\frac{109}{100}$, which are options B and E.
The two correct answers are B: $1 + \frac{9}{100}$ and E: $\frac{100}{100} + \frac{9}{100}$.
More Information
Understanding how to convert decimals to fractions helps to identify equivalent expressions more easily. Recognizing common denominators is a key skill in working with fractions.
Tips
A common mistake is misunderstanding how to convert a whole number and fraction into a single fraction. Always ensure to express whole numbers as fractions with the same denominator before adding them.
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