Convert 2.42 into a fraction in its Simplest Form
The Correct Answer and Explanation is:
Correct Answer:
2.42 = 121/50
Explanation
To convert 2.42 into a fraction in its simplest form, we follow a few straightforward steps involving place value and simplification.
Step 1: Understand the Decimal
The decimal 2.42 means:
- “2” is the whole number.
- “0.42” is the decimal part, or 42 hundredths.
So, we can write:2.42=2+0.422.42 = 2 + 0.422.42=2+0.42
Step 2: Convert the Decimal Part to a Fraction
The decimal 0.42 can be written as:0.42=421000.42 = \frac{42}{100}0.42=10042
Now we simplify this fraction.
The greatest common divisor (GCD) of 42 and 100 is 2.42÷2100÷2=2150\frac{42 \div 2}{100 \div 2} = \frac{21}{50}100÷242÷2=5021
So:0.42=21500.42 = \frac{21}{50}0.42=5021
Step 3: Add the Whole Number Back
Now add the whole number part (2) back to the simplified fraction:2+2150=2×50+2150=100+2150=121502 + \frac{21}{50} = \frac{2 \times 50 + 21}{50} = \frac{100 + 21}{50} = \frac{121}{50}2+5021=502×50+21=50100+21=50121
Step 4: Final Answer2.42=12150\boxed{2.42 = \frac{121}{50}}2.42=50121
This is already in simplest form, since 121 and 50 have no common factors other than 1.
Why This Matters
Converting decimals to fractions is important in mathematics because fractions are often more precise in calculations and can reveal number relationships more clearly. For example, fractions can help with ratios, algebraic expressions, and exact measurements in science or engineering.
Understanding how to break down a decimal into its fractional components and simplify it enhances number sense and mathematical fluency, which are critical for higher-level math.
